Mathematics · JEE

Direction ratios and direction cosines and the angle between two intersecting lines Concepts for JEE

7+ syllabus-aligned questions available

Quick answer

Master Direction ratios and direction cosines and the angle between two intersecting lines by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

Build clear conceptual foundations for Direction ratios and direction cosines and the angle between two intersecting lines before speed practice. This guide covers what JEE expects and how to test yourself with MCQs.

Concept explainer

Direction ratios and direction cosines and the angle between two intersecting lines is a core JEE Main Mathematics subtopic under Three Dimensional Geometry. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

Understand the definition and scope of Direction ratios and direction cosines and the angle between two intersecting lines in the JEE syllabus
Memorise key formulas and standard results linked to Direction ratios and direction cosines and the angle between two intersecting lines
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

Revise Direction ratios and direction cosines and the angle between two intersecting lines with a one-page formula sheet before attempting mixed tests
After each practice set, log mistakes specific to Direction ratios and direction cosines and the angle between two intersecting lines and reattempt after 48 hours

Common trap

Students often rush Direction ratios and direction cosines and the angle between two intersecting lines questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

Part of Three Dimensional Geometry in JEE Main Mathematics.

Free sample questions

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

Q4MathsUnit 11: Three Dimensional Geometry

The planes

2 x-y+4 z=5

and

5 x-

2.5 y+10 z=6

are

Q5MathsUnit 11: Three Dimensional Geometry

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

Q6MathsUnit 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

Q7MathsUnit 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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Frequently asked questions

What concepts in Direction ratios and direction cosines and the angle between two intersecting lines are essential for JEE?

Focus on core ideas across Direction ratios and direction cosines and the angle between two intersecting lines. JEE tests application, not just memorisation.