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Online Practice: Direction ratios and direction cosines and the angle between two intersecting lines 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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