A vector $\vec Q$ which has a magnitude of $8$ is added to the vector $\vec P$ which lies along $x-$ axis. The resultant of two vectors lies along $y-$ axis and has magnitude twice that of  $\vec P$. The magnitude of is $\vec P$

The magnitude of the $X$ and $Y$ component of $\vec A$ are $7$ and $6$ respectively. Also the magnitude of $X$ and $Y$ component of $\vec A + \vec B$ are $11$ and $9$ respectively. What is the magnitude of $\vec B$  ?

Find the magnitude and direction of the resultant of two vectors $A$ and $B$ in terms of their magnitudes and angle $\theta$ between them.

Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force $F_{1}$ to $F_{2}$ is $1: x$ where $x =....$

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\overrightarrow{\mathrm{A}}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is . . . . . . 

A force of $5\, N$acts on a particle along a direction making an angle of $60^°$ with vertical. Its vertical component be.......$N$