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

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Revise Direction ratios and direction cosines and the angle between two intersecting lines by covering every subtopic once, drilling formulas, then solving 7+ timed MCQs with full solutions.

Use this Direction ratios and direction cosines and the angle between two intersecting lines revision checklist before mocks and the final exam. Reinforce concepts with 7+ syllabus-aligned MCQs on Goodmarks.

Revision checklist

  1. 1.Core idea: Direction ratios and direction cosines and the angle between two intersecting lines
  2. 2.Relates to other subtopics in Three Dimensional Geometry
  3. 3.Direction ratios and cosines
  4. 4.Equation of line in 3D
  5. 5.Master Direction ratios and direction cosines and the angle between two intersecting lines definitions and standard results
  6. 6.Solve 20 timed MCQs for Direction ratios and direction cosines and the angle between two intersecting lines

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 x−2y+z−6=0\boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\boldsymbol{z}-\boldsymbol{6}=\mathbf{0} and the line x1=y2=z3\frac{x}{1}=\frac{y}{2}=\frac{z}{3} are related as
Q2MathsUnit 11: Three Dimensional Geometry
Let⁡A(2i^+3j^+5k^)B(−i^+3j^+2k^)\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(λi^+5j^+μk^)C(\lambda \hat{i}+5 \hat{j}+\mu \hat{k}) are vertices of aa triangle and its median through AA is equally inclined to the positive directions of the axes. The value of λ+\lambda+ μ\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 2x−y+4z=52 x-y+4 z=5 and 5x−5 x- 2.5y+10z=62.5 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 α,β,γ\alpha, \beta, \gamma and δ\delta with the four diagonals of a cube and A:cos⁡2α+cos⁡2β+cos⁡2γ+cos⁡2δ\mathbf{A}: \cos ^{2} \boldsymbol{\alpha}+\cos ^{2} \boldsymbol{\beta}+\cos ^{2} \boldsymbol{\gamma}+\cos ^{2} \boldsymbol{\delta} B:sin⁡2α+sin⁡2β+sin⁡2γ+sin⁡2δ\mathbf{B}: \sin ^{2} \boldsymbol{\alpha}+\sin ^{2} \boldsymbol{\beta}+\sin ^{2} \boldsymbol{\gamma}+\sin ^{2} \boldsymbol{\delta} C:cos⁡2α+cos⁡2β+cos⁡2γ+cos⁡2δ\mathbf{C}: \cos 2 \boldsymbol{\alpha}+\cos 2 \boldsymbol{\beta}+\cos 2 \gamma+\cos 2 \boldsymbol{\delta} Arrange A,B,CA, B, C in descending order
Q7MathsUnit 11: Three Dimensional Geometry
If θ\theta is the angle between the lines AB,ACA B, A C where A,B,CA, B, C are the three points with coordinates (1,2,-1),(2,0,3),(3,-1,2) respectively, then 462cos⁡θ\sqrt{462} \cos \theta is equal to

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How should I revise Direction ratios and direction cosines and the angle between two intersecting lines before JEE?

Follow the checklist on this page, revise formulas daily, and attempt mixed MCQs every 2–3 days.

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