Mathematics · JEE

Direction ratios and direction cosines and the angle between two intersecting lines Previous Year Questions for JEE

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Syllabus context

Part of Three Dimensional Geometry in JEE Main Mathematics.

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Q1MathsUnit 11: Three Dimensional Geometry

The plane

\boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\boldsymbol{z}-\boldsymbol{6}=\mathbf{0}

and the line

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}

are related as

Q2MathsUnit 11: Three Dimensional Geometry

\operatorname{Let} \boldsymbol{A}(\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\mathbf{5} \hat{\boldsymbol{k}}) \boldsymbol{B}(-\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+2 \hat{\boldsymbol{k}})

and

C(\lambda \hat{i}+5 \hat{j}+\mu \hat{k})

are vertices of

a

triangle and its median through

A

is equally inclined to the positive directions of the axes. The value of

\lambda+

\mu

is equal to

Q3MathsUnit 11: Three Dimensional Geometry

The direction ratios of the joining

A(1,2,1)

and (2,1,2) are

Q4MathsUnit 11: Three Dimensional Geometry

The projection of the line segment joining (0,0,0) and (5,2,4) on the line whose direction ratios are 2,-3,6 is

Q5MathsUnit 11: Three Dimensional Geometry

The planes

2 x-y+4 z=5

and

5 x-

2.5 y+10 z=6

are

Q6MathsUnit 11: Three Dimensional Geometry

The number of straight lines that are equally inclined to the threedimensional coordinate axes, is

Q7MathsUnit 11: Three Dimensional Geometry

If a ray makes angles

\alpha, \beta, \gamma

and

\delta

with the four diagonals of a cube and

\mathbf{A}: \cos ^{2} \boldsymbol{\alpha}+\cos ^{2} \boldsymbol{\beta}+\cos ^{2} \boldsymbol{\gamma}+\cos ^{2} \boldsymbol{\delta}

\mathbf{B}: \sin ^{2} \boldsymbol{\alpha}+\sin ^{2} \boldsymbol{\beta}+\sin ^{2} \boldsymbol{\gamma}+\sin ^{2} \boldsymbol{\delta}

\mathbf{C}: \cos 2 \boldsymbol{\alpha}+\cos 2 \boldsymbol{\beta}+\cos 2 \gamma+\cos 2 \boldsymbol{\delta}

Arrange

A, B, C

in descending order

Q8MathsUnit 11: Three Dimensional Geometry

\theta

is the angle between the lines

A B, A C

where

A, B, C

are the three points with coordinates (1,2,-1),(2,0,3),(3,-1,2) respectively, then

\sqrt{462} \cos \theta

is equal to

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Why practise PYQs for Direction ratios and direction cosines and the angle between two intersecting lines?

PYQs reveal recurring concepts, common traps, and the difficulty level JEE expects. Solving them builds exam temperament and time management.

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Our bank includes exam-style MCQs aligned with JEE Main Mathematics syllabus for Direction ratios and direction cosines and the angle between two intersecting lines, covering the same topics as previous year papers.

How should I use PYQs for Three Dimensional Geometry?

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