The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

Given $A = 2 \hat{i} + \hat{j}$,$B = 3 \hat{j} - \hat{k}$,and $C = 6 \hat{i} - 2 \hat{k}$. The value of $A - 2B + 3C$ is:

The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ has a magnitude $R_{1}$. If the direction of $\overrightarrow{Q}$ is reversed,the resultant has a magnitude $R_{2}$. The value of $(R_{1}^{2} + R_{2}^{2})$ is:

The angle $\beta$ between vector $\overrightarrow{A}$ and the resultant vector $(\overrightarrow{A}-\overrightarrow{B})$ is given by:

Which vector must be added to the resultant vector $\vec{P} = 2\hat{i} + 7\hat{j} - 10\hat{k}$ and $\vec{Q} = \hat{i} + 2\hat{j} + 3\hat{k}$ to obtain a unit vector along the $X$-axis?

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 $\vec{Q}$.