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

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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

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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?

Solve timed sets, review every explanation, note weak subtopics, then revisit with focused practice on Goodmarks.

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