If $|\vec A + \vec B| = |\vec A| + |\vec B|$,then the angle between $\vec A$ and $\vec B$ will be ....... $^o$.

$A$ mosquito is moving with a velocity $\overrightarrow{v} = 0.5t^2 \hat{i} + 3t \hat{j} + 9 \hat{k} \, m/s$. What will be the direction of the mosquito after $t = 2 \, s$?

If the angle between unit vectors $\hat{a}$ and $\hat{b}$ is $60^{\circ}$, which of the following vectors have a magnitude of $1$?
$(A)$ $\frac{\hat{a} + \hat{b}}{\sqrt{3}}$
$(B)$ $\hat{a} + \hat{b}$
$(C)$ $\hat{a}$
$(D)$ $\hat{b}$

$A$ particle moves from point $P (2, 3, 5)$ to point $Q (3, 4, 5)$. The displacement vector is:

$A$ force,$\vec{F}=(4 \hat{i}+3 \hat{j}-5 \hat{k}) \text{ N}$,is acting on a body. If the horizontal direction is taken along the $\hat{i} + \hat{j}$ direction,find the angle $\theta$ that the force makes with this horizontal direction.

The values of $x$ and $y$ for which vectors $\vec{A} = (6\hat{i} + x\hat{j} - 2\hat{k})$ and $\vec{B} = (5\hat{i} - 6\hat{j} - y\hat{k})$ may be parallel are