Class 12

THREE DIMENSIONAL GEOMETRY question bank (Maths)

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Q1.

If $OP = 8$ and $\overrightarrow{OP}$ makes angles $45^\circ$ and $60^\circ$ with the $OX$-axis and $OY$-axis respectively,then $\overrightarrow{OP} =$

(A)

$8(\sqrt{2}\hat{i} + \hat{j} \pm \hat{k})$

(B)

$4(\sqrt{2}\hat{i} + \hat{j} \pm \hat{k})$

(C)

$\frac{1}{4}(\sqrt{2}\hat{i} + \hat{j} \pm \hat{k})$

(D)

$\frac{1}{8}(\sqrt{2}\hat{i} + \hat{j} \pm \hat{k})$

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Q2.

The direction cosines of the line $x = y = z$ are

(A)

$\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$

(B)

$\frac{1}{3}, \frac{1}{3}, \frac{1}{3}$

(C)

$1, 1, 1$

(D)

None of these

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