$A$ football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is:

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

The resultant $\vec{R}$ of $\vec{P}$ and $\vec{Q}$ is perpendicular to $\vec{P}$. Also,$|\vec{P}| = |\vec{R}|$. Find the angle between $\vec{P}$ and $\vec{Q}$.

Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $n$ times the magnitude of $(\vec A - \vec B)$. The angle between $\vec A$ and $\vec B$ is

$A$ particle moves $21 \ m$ along the direction of the vector $6\hat{i} + 2\hat{j} + 3\hat{k}$,then it moves $14 \ m$ along the direction of the vector $3\hat{i} - 2\hat{j} + 6\hat{k}$. What is its total displacement (in meters)?

$A$ force of $6\,N$ and another of $8\,N$ can be applied together to produce the effect of a single force of $..........\,N$