How much of JEE Main comes from Three-Dimensional Geometry?

JEEGenie estimates about 5% of JEE Main marks come from Three-Dimensional Geometry, based on recent papers. The share varies from year to year.

Which formulas matter most in Three-Dimensional Geometry?

The Three-Dimensional Geometry sheet on this page has 24 formula entries, starting with Direction Cosines (DC) of a Line, Direction Ratios (DR) of a Line, Angle Between Two Lines (using DCs/DRs), Condition for Perpendicular and Parallel Lines, Equation of a Line in Space: Vector Form. Each one comes with when to use it and the trap to avoid.

What topics does Three-Dimensional Geometry cover for JEE?

Three-Dimensional Geometry covers Direction Cosines and Ratios, Line in Space, Plane in Space, Angle Between Lines and Planes, Shortest Distance, Coplanarity.

How should I revise Three-Dimensional Geometry before the exam?

Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Three-Dimensional Geometry questions on JEEGenie.

How many previous-year questions are there on Three-Dimensional Geometry?

JEEGenie has 498 previous-year questions on Three-Dimensional Geometry, and this page shows a few with worked explanations.

Is practice on Three-Dimensional Geometry free on JEEGenie?

Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.

Three-Dimensional Geometry for JEE Main & Advanced — formulas, what is asked, and traps

JEEGenie estimates about 5% of JEE Main marks come from Three-Dimensional Geometry. This page covers 24 formula entries, each with when to use it, what JEE asks and the traps. A common slip: Direction cosines are always for a directed line; reversing the direction changes signs of all three.

Key points to know

Direction Cosines (DC) of a Line. Direction cosines are the cosines of the angles a line makes with the positive x, y, and z axes. They are denoted by l, m, n and satisfy l² + m² + n² = 1.
Direction Ratios (DR) of a Line. Direction ratios are any three numbers proportional to the direction cosines. If a line has DRs a, b, c, then its DCs are ±(a/√(a²+b²+c²), b/√(...), c/√(...)).
Equation of a Line in Space: Vector Form. A line through a point with position vector a and parallel to vector b is given by r = a + λb, where λ is a scalar parameter.
Equation of a Line in Space: Cartesian Form (Symmetric). If a line passes through (x₁,y₁,z₁) and has DRs a,b,c, its symmetric equation is (x-x₁)/a = (y-y₁)/b = (z-z₁)/c = λ.
Equation of a Plane: General Form. A plane in 3D is given by ax + by + cz + d = 0, where (a,b,c) are the direction ratios of the normal to the plane.
Equation of a Plane: Intercept Form. If a plane cuts the x, y, z axes at a, b, c respectively, its equation is x/a + y/b + z/c = 1.
Equation of a Plane: Normal Form. A plane at distance p from origin with unit normal vector (l,m,n) is lx + my + nz = p.
Equation of a Plane Through a Given Point and Parallel to Two Lines. A plane through point (x₁,y₁,z₁) and parallel to lines with DRs (a₁,b₁,c₁) and (a₂,b₂,c₂) has normal vector perpendicular to both DRs, found via cross product.

Formula sheet

Name	Formula	When to use
Direction Cosines (DC) of a Line	$l = \cos α, m = \cos β, n = \cos γ$	Use when you need the actual angles a line makes with axes or to find the line's orientation uniquely.
Direction Ratios (DR) of a Line	$DRs: a, b, c \Rightarrow (l, m, n) = \pm \frac{(a, b, c)}{\sqrt{a^{2} + b^{2} + c^{2}}}$ (one common sign for all three)	Use when you have a vector along the line (e.g., from two points) and need to find DCs or check parallelism.
Angle Between Two Lines (using DCs/DRs)	$\cos θ = ∣ l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2} ∣ = \frac{∣ a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} ∣}{\sqrt{a_{1}^{2} + b_{1}^{2} + c_{1}^{2}} \sqrt{a_{2}^{2} + b_{2}^{2} + c_{2}^{2}}}$	Use to find the angle between any two lines given their DCs or DRs.
Condition for Perpendicular and Parallel Lines	$Perpendicular: a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0 Parallel: \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$	Use to quickly check geometric relationships between lines in 3D.
Equation of a Line in Space: Vector Form	$\vec{r} = \vec{a} + λ \vec{b}$	Use when you know a point on the line and its direction (e.g., from a parallel vector).
Equation of a Line in Space: Cartesian Form (Symmetric)	$\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c} = λ$	Use when coordinates of a point and direction ratios are known; common in JEE problems.
Equation of Line Through Two Points	$\frac{x - x_{1}}{x_{2} - x_{1}} = \frac{y - y_{1}}{y_{2} - y_{1}} = \frac{z - z_{1}}{z_{2} - z_{1}}$	Use when two points on the line are given.
Equation of a Plane: General Form	$a x + b y + c z + d = 0$	Use as the standard form to represent any plane; often used to find distance from a point.
Equation of a Plane: Intercept Form	$\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$	Use when the intercepts on axes are given or easily found.
Equation of a Plane: Normal Form	$l x + m y + n z = p$	Use to find the perpendicular distance from origin to a plane.
Angle Between Two Planes	$\cos θ = \frac{∣ a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} ∣}{\sqrt{a_{1}^{2} + b_{1}^{2} + c_{1}^{2}} \sqrt{a_{2}^{2} + b_{2}^{2} + c_{2}^{2}}}$	Use to find the dihedral angle between two planes.
Condition for Perpendicular and Parallel Planes	$Perpendicular: a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0 Parallel: \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$	Use to check geometric relationships between planes.
Distance of a Point from a Plane	$Distance = \frac{∣ a x_{1} + b y_{1} + c z_{1} + d ∣}{\sqrt{a^{2} + b^{2} + c^{2}}}$	Use to find the shortest distance from a point to a plane.
Distance Between Two Parallel Planes	$Distance = \frac{∣ d_{1} - d_{2} ∣}{\sqrt{a^{2} + b^{2} + c^{2}}}$	Use when given two parallel planes.
Equation of a Plane Through a Given Point and Parallel to Two Lines	$∣ \begin{array}{ccc} x - x_{1} & y - y_{1} & z - z_{1} \\ a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \end{array} ∣ = 0$	Use when a plane is defined by a point and two direction vectors (e.g., containing two lines).
Equation of a Plane Through Three Points	$∣ \begin{array}{ccc} x - x_{1} & y - y_{1} & z - z_{1} \\ x_{2} - x_{1} & y_{2} - y_{1} & z_{2} - z_{1} \\ x_{3} - x_{1} & y_{3} - y_{1} & z_{3} - z_{1} \end{array} ∣ = 0$	Use when three points on the plane are given.
Angle Between a Line and a Plane	$\sin ϕ = \frac{∣ a A + b B + c C ∣}{\sqrt{a^{2} + b^{2} + c^{2}} \sqrt{A^{2} + B^{2} + C^{2}}}$	Use to find the angle at which a line meets a plane.
Condition for a Line to Lie in a Plane	$Line: \frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}, Plane: A x + B y + C z + D = 0 Conditions: a A + b B + c C = 0 and A x_{1} + B y_{1} + C z_{1} + D = 0$	Use to check if a given line is contained in a plane.
Shortest Distance Between Two Skew Lines	$SD = \frac{∣ ({\vec{a}}_{2} - {\vec{a}}_{1}) \cdot ({\vec{b}}_{1} \times {\vec{b}}_{2}) ∣}{∣ {\vec{b}}_{1} \times {\vec{b}}_{2} ∣}$	Use to find the shortest distance between two lines that are not parallel and do not intersect.
Shortest Distance Between Two Parallel Lines	$Distance = \frac{∣ ({\vec{a}}_{2} - {\vec{a}}_{1}) \times \vec{b} ∣}{∣ \vec{b} ∣}$	Use when two lines are parallel (DRs proportional).
Intersection of a Line and a Plane	$Line: \frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c} = λ Plane: A x + B y + C z + D = 0 \Rightarrow A (x_{1} + λ a) + B (y_{1} + λ b) + C (z_{1} + λ c) + D = 0$	Use to find the point where a line meets a plane.
Foot of Perpendicular from a Point to a Plane	$t = \frac{a x_{1} + b y_{1} + c z_{1} + d}{a^{2} + b^{2} + c^{2}} Foot: (x_{1} - a t, y_{1} - b t, z_{1} - c t)$	Use to find the projection of a point onto a plane.
Image of a Point in a Plane	$Image: (x_{1} - 2 a t, y_{1} - 2 b t, z_{1} - 2 c t) with t = \frac{a x_{1} + b y_{1} + c z_{1} + d}{a^{2} + b^{2} + c^{2}}$	Use to find the mirror image of a point across a plane.
Coplanarity of Two Lines	$Lines: \vec{r} = {\vec{a}}_{1} + λ {\vec{b}}_{1}, \vec{r} = {\vec{a}}_{2} + μ {\vec{b}}_{2} Coplanar if ({\vec{a}}_{2} - {\vec{a}}_{1}) \cdot ({\vec{b}}_{1} \times {\vec{b}}_{2}) = 0$	Use to check if two given lines lie in the same plane.

Open the Three-Dimensional Geometry formula page

What JEE asks

Direction Cosines (DC) of a Line. JEE often asks to find DCs from a given vector or to verify l²+m²+n²=1 in multiple-choice questions.
Direction Ratios (DR) of a Line. JEE frequently tests conversion between DRs and DCs, especially in problems involving angles between lines.
Angle Between Two Lines (using DCs/DRs). JEE often asks for the angle between lines given in symmetric form or vector form, sometimes combined with condition for perpendicularity (cosθ=0).
Condition for Perpendicular and Parallel Lines. JEE often tests these conditions in problems involving shortest distance or finding a line perpendicular to two given lines.
Equation of a Line in Space: Vector Form. JEE often gives lines in vector form and asks for intersection or distance problems.
Equation of a Line in Space: Cartesian Form (Symmetric). JEE often asks to convert between vector and Cartesian forms, or to find the line through two points.
Equation of Line Through Two Points. JEE often tests this as a direct formula application or in problems involving intersection with a plane.
Equation of a Plane: General Form. JEE frequently asks to find the equation of a plane given conditions like passing through three points or perpendicular to a line.
Equation of a Plane: Intercept Form. JEE often asks to convert general form to intercept form to find intercepts quickly.
Equation of a Plane: Normal Form. JEE often tests conversion from general form to normal form to find p.
Angle Between Two Planes. JEE often asks for the angle between planes given in general form, or condition for perpendicularity (cosθ=0).
Condition for Perpendicular and Parallel Planes. JEE often tests these in problems involving distance between parallel planes or finding a plane perpendicular to two given planes.
Distance of a Point from a Plane. JEE often asks this directly or in problems involving spheres or loci.
Distance Between Two Parallel Planes. JEE often tests this as a quick formula application.
Equation of a Plane Through a Given Point and Parallel to Two Lines. JEE often asks to find the plane containing two intersecting or parallel lines.
Equation of a Plane Through Three Points. JEE often tests this as a direct method or in problems involving intersection of lines.
Angle Between a Line and a Plane. JEE often asks this in problems involving line-plane intersection or shortest distance.
Condition for a Line to Lie in a Plane. JEE often tests this in problems involving intersection of line and plane or finding the plane containing a line.
Shortest Distance Between Two Skew Lines. JEE often asks for the shortest distance between skew lines given in vector or Cartesian form.
Shortest Distance Between Two Parallel Lines. JEE often tests this as a simpler variant of the skew line problem.
Intersection of a Line and a Plane. JEE often asks this in problems involving foot of perpendicular or reflection.
Foot of Perpendicular from a Point to a Plane. JEE often tests this in problems involving reflection of a point across a plane.
Image of a Point in a Plane. JEE often asks for the image of a point or a line in a plane.
Coplanarity of Two Lines. JEE often tests this in problems involving finding the plane containing two lines.

Common traps

Direction cosines are always for a directed line; reversing the direction changes signs of all three. Direction Cosines (DC) of a Line
Direction ratios are not unique; any scalar multiple gives the same line. Direction Ratios (DR) of a Line
For acute angle, take absolute value; for obtuse, use negative sign. Angle Between Two Lines (using DCs/DRs)
For perpendicular, use the dot product of DRs (not DCs) directly; no absolute value needed. Condition for Perpendicular and Parallel Lines
The direction vector b must be non-zero; λ is any real number. Equation of a Line in Space: Vector Form
If any DR is zero (e.g., a=0), the equation becomes x = x₁ (constant), and the other ratios still hold. Equation of a Line in Space: Cartesian Form (Symmetric)
If any coordinate difference is zero, treat that numerator as zero (e.g., x = x₁). Equation of Line Through Two Points
The coefficients a,b,c are not unique; multiplying by a constant gives the same plane. Equation of a Plane: General Form
Intercepts can be negative if the plane cuts the negative axes. Equation of a Plane: Intercept Form
The normal vector must be a unit vector; otherwise, divide by its magnitude. Equation of a Plane: Normal Form
Take absolute value for acute angle; for obtuse, use negative. Angle Between Two Planes
For parallel planes, the constant term d may differ; that gives distinct parallel planes. Condition for Perpendicular and Parallel Planes
Use absolute value; distance is always non-negative. Distance of a Point from a Plane
The planes must have the same normal coefficients (a,b,c); otherwise, they are not parallel. Distance Between Two Parallel Planes

Topics in Three-Dimensional Geometry

Direction Cosines and Ratios
Line in Space
Plane in Space
Angle Between Lines and Planes
Shortest Distance
Coplanarity

Previous-year questions on Three-Dimensional Geometry

JEEGenie has 498 previous-year questions on Three-Dimensional Geometry. A few worked examples follow.

Year	Questions
2026	29
2025	35
2024	47
2023	73
2022	49
2021	54
2020	19
2019	58
2018	13
2017	11
2016	11
2015	11
2014	10
2013	10
2012	11
2011	2
2010	6
2009	5
2008	6
2007	6
2006	4
2005	7
2004	10
2003	8
2002	2
1985	1

Question 1 medium

If the point of intersection of the lines

\frac{x + 1}{3} = \frac{y + a}{5} = \frac{z + b + 1}{7}

and

\frac{x - 2}{1} = \frac{y - b}{4} = \frac{z - 2 a}{7}

lies on xy-plane, then the value of

a + b

is:

Answer: C

Explanation. Let the first line be

\frac{x + 1}{3} = \frac{y + a}{5} = \frac{z + b + 1}{7} = t

x = 3 t - 1, y = 5 t - a, z = 7 t - b - 1.

Let the second line be

\frac{x - 2}{1} = \frac{y - b}{4} = \frac{z - 2 a}{7} = s

x = s + 2, y = 4 s + b, z = 7 s + 2 a .

At intersection, equate coordinates:

3 t - 1 = s + 2 ⟹ s = 3 t - 3,

5 t - a = 4 s + b ⟹ 5 t - a = 4 (3 t - 3) + b = 12 t - 12 + b,

7 t - b - 1 = 7 s + 2 a = 7 (3 t - 3) + 2 a = 21 t - 21 + 2 a .

From the

y

-equation:

\begin{matrix} 5 t - a = 12 t - 12 + b ⟹ - 7 t - a - b = - 12 ⟹ 7 t + a + b = 12. & (1) \end{matrix}

From the

z

-equation:

\begin{matrix} 7 t - b - 1 = 21 t - 21 + 2 a ⟹ - 14 t - 2 a - b = - 20 ⟹ 14 t + 2 a + b = 20. & (2) \end{matrix}

Subtract (1) from (2):

\begin{matrix} (14 t + 2 a + b) - (7 t + a + b) = 20 - 12 ⟹ 7 t + a = 8. & (3) \end{matrix}

From (1) and (3): Subtract (3) from (1):

(7 t + a + b) - (7 t + a) = 12 - 8 ⟹ b = 4.

Now the intersection lies on the

x y

-plane, so

z = 0

7 t - b - 1 = 0 ⟹ 7 t - 4 - 1 = 0 ⟹ 7 t = 5 ⟹ t = \frac{5}{7} .

From (3):

7 (\frac{5}{7}) + a = 8 ⟹ 5 + a = 8 ⟹ a = 3.

Thus

a + b = 3 + 4 = 7.

C

From NTA/IIT papers: JEE Main 2026 · 2 Apr Shift 1

Question 2 hard

Line

L_{1}

passes through the point

(1, 2, 3)

and is parallel to

z

-axis. Line

L_{2}

passes through the point

(λ, 5, 6)

and is parallel to

y

-axis. Let for

λ = λ_{1}, λ_{2}, λ_{2} < λ_{1}

, the shortest distance between the two lines be 3 . Then the square of the distance of the point

(λ_{1}, λ_{2}, 7)

from the line

L_{1}

Answer: A

Explanation.

L_{1}

: through

(1, 2, 3)

, parallel to

z

-axis, so direction

(0, 0, 1)

L_{2}

: through

(λ, 5, 6)

, parallel to

y

-axis, so direction

(0, 1, 0)

. Shortest distance between skew lines: Vector between points:

(λ - 1, 3, 3)

. Cross product of directions:

(0, 0, 1) \times (0, 1, 0) = (- 1, 0, 0)

, magnitude

1

. Distance =

\frac{∣ (λ - 1, 3, 3) \cdot (- 1, 0, 0) ∣}{1} = ∣ λ - 1 ∣

. Given

∣ λ - 1 ∣ = 3

, so

λ = 4

λ = - 2

. Thus

λ_{1} = 4

λ_{2} = - 2

. Point

P = (4, - 2, 7)

. Distance from

P

L_{1}

L_{1}

passes through

(1, 2, 3)

, direction

(0, 0, 1)

. Vector from point on

L_{1}

P

(3, - 4, 4)

. Project onto direction:

(0, 0, 4)

. Perpendicular component:

(3, - 4, 0)

. Distance =

\sqrt{3^{2} + (- 4)^{2}} = 5

. Square =

25

. Answer is option A.

From NTA/IIT papers: JEE Main 2025 · 3 Apr Shift 1

Question 3 easy

The shortest distance between the lines

\frac{x - 3}{2} = \frac{y + 15}{- 7} = \frac{z - 9}{5}

and

\frac{x + 1}{2} = \frac{y - 1}{1} = \frac{z - 9}{- 3}

$8 \sqrt{3}$
$6 \sqrt{3}$
$5 \sqrt{3}$
$4 \sqrt{3}$

Answer: D

Explanation. Line 1 passes through

A = (3, - 15, 9)

with direction

\vec{b_{1}} = (2, - 7, 5)

. Line 2 passes through

B = (- 1, 1, 9)

with direction

\vec{b_{2}} = (2, 1, - 3)

. Step 1: Compute

\vec{b_{1}} \times \vec{b_{2}}

\vec{b_{1}} \times \vec{b_{2}} = ∣ \begin{array}{ccc} \vec{i} & \vec{j} & \vec{k} \\ 2 & - 7 & 5 \\ 2 & 1 & - 3 \end{array} ∣ = \vec{i} [(- 7) (- 3) - (5) (1)] - \vec{j} [(2) (- 3) - (5) (2)] + \vec{k} [(2) (1) - (- 7) (2)] = \vec{i} [21 - 5] - \vec{j} [- 6 - 10] + \vec{k} [2 + 14] = (16, 16, 16)

Step 2: Magnitude of

\vec{b_{1}} \times \vec{b_{2}}

∣ \vec{b_{1}} \times \vec{b_{2}} ∣ = \sqrt{16^{2} + 16^{2} + 16^{2}} = 16 \sqrt{3}

Step 3: Compute

\vec{A B} = B - A = (- 1 - 3, 1 - (- 15), 9 - 9) = (- 4, 16, 0)

. Step 4: Shortest distance formula:

d = \frac{∣ \vec{A B} \cdot (\vec{b_{1}} \times \vec{b_{2}}) ∣}{∣ \vec{b_{1}} \times \vec{b_{2}} ∣} \vec{A B} \cdot (16, 16, 16) = (- 4) (16) + (16) (16) + (0) (16) = - 64 + 256 + 0 = 192 d = \frac{∣ 192 ∣}{16 \sqrt{3}} = \frac{192}{16 \sqrt{3}} = \frac{12}{\sqrt{3}} = \frac{12 \sqrt{3}}{3} = 4 \sqrt{3}

The shortest distance is

4 \sqrt{3}

From NTA/IIT papers: JEE Main 2024 · 6 Apr Shift 1

Question 4 medium

If the equation of the plane passing through the line of intersection of the planes

2 x - y + z = 3, 4 x - 3 y + 5 z + 9 = 0

and parallel to the line

\frac{x + 1}{- 2} = \frac{y + 3}{4} = \frac{z - 2}{5}

a x + b y + c z + 6 = 0

, then

a + b + c

is equal to :

Answer: C

Explanation. Let the required plane pass through the line of intersection of the planes

2 x - y + z - 3 = 0

and

4 x - 3 y + 5 z + 9 = 0.

Any plane through their line of intersection is of the form

(2 x - y + z - 3) + λ (4 x - 3 y + 5 z + 9) = 0.

Simplifying,

(2 + 4 λ) x + (- 1 - 3 λ) y + (1 + 5 λ) z + (- 3 + 9 λ) = 0.

This plane is parallel to the line

\frac{x + 1}{- 2} = \frac{y + 3}{4} = \frac{z - 2}{5},

whose direction ratios are

(- 2, 4, 5)

. For the plane to be parallel to the line, the normal to the plane must be perpendicular to the line’s direction vector. Hence,

(2 + 4 λ) (- 2) + (- 1 - 3 λ) (4) + (1 + 5 λ) (5) = 0.

Compute:

- 4 - 8 λ - 4 - 12 λ + 5 + 25 λ = 0

(- 4 - 4 + 5) + (- 8 λ - 12 λ + 25 λ) = 0

- 3 + 5 λ = 0

λ = \frac{3}{5} .

Substitute

λ = \frac{3}{5}

into the plane equation: Coefficient of

x

2 + 4 \cdot \frac{3}{5} = 2 + \frac{12}{5} = \frac{22}{5} .

Coefficient of

y

- 1 - 3 \cdot \frac{3}{5} = - 1 - \frac{9}{5} = - \frac{14}{5} .

Coefficient of

z

1 + 5 \cdot \frac{3}{5} = 1 + 3 = 4 = \frac{20}{5} .

Constant term:

- 3 + 9 \cdot \frac{3}{5} = - 3 + \frac{27}{5} = \frac{- 15 + 27}{5} = \frac{12}{5} .

So the plane is

\frac{22}{5} x - \frac{14}{5} y + 4 z + \frac{12}{5} = 0.

Multiply through by

5

22 x - 14 y + 20 z + 12 = 0.

Divide by

2

11 x - 7 y + 10 z + 6 = 0.

Comparing with

a x + b y + c z + 6 = 0,

we get

a = 11, b = - 7, c = 10.

Thus,

a + b + c = 11 - 7 + 10 = 14.

Answer: (C)

From NTA/IIT papers: JEE Main 2023 · 6 Apr Shift 1

Frequently asked questions

How much of JEE Main comes from Three-Dimensional Geometry?: JEEGenie estimates about 5% of JEE Main marks come from Three-Dimensional Geometry, based on recent papers. The share varies from year to year.
Which formulas matter most in Three-Dimensional Geometry?: The Three-Dimensional Geometry sheet on this page has 24 formula entries, starting with Direction Cosines (DC) of a Line, Direction Ratios (DR) of a Line, Angle Between Two Lines (using DCs/DRs), Condition for Perpendicular and Parallel Lines, Equation of a Line in Space: Vector Form. Each one comes with when to use it and the trap to avoid.
What topics does Three-Dimensional Geometry cover for JEE?: Three-Dimensional Geometry covers Direction Cosines and Ratios, Line in Space, Plane in Space, Angle Between Lines and Planes, Shortest Distance, Coplanarity.
How should I revise Three-Dimensional Geometry before the exam?: Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Three-Dimensional Geometry questions on JEEGenie.
How many previous-year questions are there on Three-Dimensional Geometry?: JEEGenie has 498 previous-year questions on Three-Dimensional Geometry, and this page shows a few with worked explanations.
Is practice on Three-Dimensional Geometry free on JEEGenie?: Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.