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Vector Algebra

Multiple Choice Questions

51.

Let A be a point in space such that $|OA| = 12$ where O is the origin. If $OA$ is inclined at angles 45^o and 60⁰ with x-axis and y-axis respectively, then what is $OA$ equal to ?

$6 \hat{j} + 6 \hat{i} + 2 \hat{k}$
$6 \sqrt{2} \hat{i} + 6 \hat{j} \pm 6 \hat{k}$
$6 \sqrt{2} \hat{j} + 6 \hat{i} \pm 6 \hat{k}$
$3 \sqrt{2} \hat{j} + 3 \hat{i} \pm 6 \hat{k}$

52.
If $\hat{a}$ is a unit vector in the xy-plane making an angle 30^o with the positive x-axis, then what $\hat{a}$ is equal to

$\frac{\sqrt{3} \hat{i} + \hat{j}}{2}$

$\frac{\sqrt{3} \hat{i} - \hat{j}}{2}$

$\frac{\hat{i} + \sqrt{3} \hat{j}}{2}$

$\frac{\hat{i} - \sqrt{3} \hat{j}}{2}$

$\frac{\sqrt{3} \hat{i} + \hat{j}}{2}$

$\hat{a} is defined as \hat{a} = |\vec{a}| \cos (θ) \hat{i} + |\vec{a}| \sin (θ) \hat{j} where θ is angle made with x - axis = (1) \cos (30 °) \hat{i} + (1) \sin (30 °) \hat{j} = \frac{\sqrt{3} \hat{i} + 1 \hat{j}}{2}$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

52. If a^ is a unit vector in the xy-plane making an angle 30o with the positive x-axis, then what a^ is equal to 3i^ + j^2 3i^ - j^2 i^ + 3j^2 i^ - 3 j^2

52.
If $\hat{a}$ is a unit vector in the xy-plane making an angle 30^o with the positive x-axis, then what $\hat{a}$ is equal to

$\frac{\sqrt{3} \hat{i} + \hat{j}}{2}$

$\frac{\sqrt{3} \hat{i} - \hat{j}}{2}$

$\frac{\hat{i} + \sqrt{3} \hat{j}}{2}$

$\frac{\hat{i} - \sqrt{3} \hat{j}}{2}$