What vector must be added to the two vectors $\hat{i} - 2\hat{j} + 2\hat{k}$ and $2\hat{i} + \hat{j} - \hat{k}$ so that the resultant may be a unit vector along the $X$-axis?

The figure shows three vectors $p$,$q$,and $r$,where $C$ is the midpoint of $AB$. Which of the following relations is correct?

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

Forces $F_1$ and $F_2$ act on a point mass in two mutually perpendicular directions. The resultant force on the point mass will be

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ have equal magnitudes. If the magnitude of $\overrightarrow{A} + \overrightarrow{B}$ is equal to two times the magnitude of $\overrightarrow{A} - \overrightarrow{B}$,then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ will be .......................

$A$ car travels a distance of $6 \, km$ at an angle of $45^\circ$ with the East,and then travels a distance of $4 \, km$ at an angle of $135^\circ$ with the East. What is the distance from the origin?