When vector $\overrightarrow{A} = 2\hat{i} + 3\hat{j} + 2\hat{k}$ is subtracted from vector $\vec{B}$,it gives a vector equal to $2\hat{j}$. Then the magnitude of vector $\vec{B}$ will be:

$A$ vector $P$ has $X$ and $Y$ components of magnitude $2$ units and $4$ units respectively. $A$ vector $Q$ along the negative $X$-axis has a magnitude of $6$ units. The vector $(Q - P)$ will be

The resultant $\vec{R}$ of $\vec{P}$ and $\vec{Q}$ is perpendicular to $\vec{P}$. Also,$|\vec{P}| = |\vec{R}|$. Find the angle between $\vec{P}$ and $\vec{Q}$.

$A$ bus is moving on a straight road towards north with a uniform speed of $50 \; km/h$. Then it turns left through $90^{\circ}$. If the speed remains unchanged after turning,the increase in the velocity of the bus in the turning process is:

The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is

Given $A = 2 \hat{i} + \hat{j}$,$B = 3 \hat{j} - \hat{k}$,and $C = 6 \hat{i} - 2 \hat{k}$. The value of $A - 2B + 3C$ is: