If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors,the angle between these vectors is ........ $^o$.

Let $\vec{P} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{Q} = -(\hat{i} + \hat{j} + \hat{k})$. The angle between $(\vec{P} - \vec{Q})$ and $\vec{P}$ is (in $^\circ$)

If the square of the resultant of two forces of equal magnitude is equal to three times their product,then the angle between them is ........ $^o$.

$A$ car travels $6 \, km$ at an angle of $45^\circ$ north of east and then travels $4 \, km$ at an angle of $135^\circ$ north of east. How far is the final point from the starting point? What angle does the straight line joining its initial and final position make with the east?

$A$ vector of length $\ell$ is turned by an angle $\theta$. Find the change in the position vector of the tip.

If the direction of a vector $\overrightarrow{A}$ is reversed,find $\Delta \overrightarrow{A}$ and $|\Delta \overrightarrow{A}|$.