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Mathematics · JEE

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

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Quick answer

Short tricks for Direction ratios and direction cosines and the angle between two intersecting lines work only with strong fundamentals. Apply the tips below in timed sets and review every explanation.

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Short tricks for speed

  • Direction ratios and direction cosines and the angle between two intersecting lines focus drill

    Solve 15 mixed MCQs for Direction ratios and direction cosines and the angle between two intersecting lines, review every explanation, and note formulas you hesitated on.

  • Calculus substitution scan

    Spot standard forms (sin²x, 1/(a²+x²), e^ax) before integrating — JEE rewards pattern recognition.

  • Graph sketch shortcut

    For coordinate geometry, mark intercepts and asymptotes first; many MCQs need only qualitative graph features.

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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Are short tricks enough for Direction ratios and direction cosines and the angle between two intersecting lines in JEE?

No — tricks complement concepts. Master the theory first, then use shortcuts in timed MCQ practice.

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