The vectors $(\vec{A} + \vec{B})$ and $(\vec{A} - \vec{B})$ are perpendicular to each other. This is possible under the condition:

$\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors of equal magnitudes and $\theta$ is the angle between them. The angle between $\overrightarrow{A}$ or $\overrightarrow{B}$ with their resultant is

The magnitudes of pairs of displacement vectors are given. Which pair of displacement vectors cannot be added to give a resultant vector of magnitude $13 \, cm$?

The resultant of $\overrightarrow P$ and $\overrightarrow Q$ is perpendicular to $\overrightarrow P$. What is the angle between $\overrightarrow P$ and $\overrightarrow Q$?

The sum of the magnitudes of two forces acting at a point is $16 \,N$. If their resultant is normal to the smaller force and has a magnitude of $8 \,N$, then the forces are:

$A$ 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?