Two vectors $\vec{A}$ and $\vec{B}$ have magnitudes $3 \text{ units}$ and $4 \text{ units}$ respectively. If the angle between them is $60^{\circ}$,find the magnitude of their resultant vector.

$A$ car travels $6 \, km$ at an angle of $45^o$ north of east and then travels a distance of $4 \, km$ at an angle of $135^o$ 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 direction?

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

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 ........ $^o$.

Two vectors $\vec A$ and $\vec B$ have magnitudes $2$ and $1$ respectively. If the angle between $\vec A$ and $\vec B$ is $60^{\circ}$,then which of the following vectors may be equal to $\frac{\vec A}{2} - \vec B$?

What displacement must be added to the displacement $25\hat{i} - 6\hat{j} \text{ m}$ to give a resultant displacement of $7.0 \text{ m}$ pointing in the $X$-direction?