For non-zero vectors $a$ and $b$,if $|a+b| < |a-b|$,then $a$ and $b$ are

If the components of $\vec{a}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}$ along and perpendicular to $\vec{b}=3 \hat{i}+\hat{j}-\hat{k}$ respectively,are $\frac{16}{11}(3 \hat{i}+\hat{j}-\hat{k})$ and $\frac{1}{11}(-4 \hat{i}-5 \hat{j}-17 \hat{k})$,then $\alpha^2+\beta^2+\gamma^2$ is equal to :

If $P=(0,1,2), Q=(4,-2,1)$ and $O=(0,0,0)$,then $\angle POQ=$

If $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$,$|\vec{a}|=3$,$|\vec{b}|=5$,and $|\vec{c}|=7$,then the angle between $\vec{a}$ and $\vec{b}$ is

If $a\hat{i} + 6\hat{j} - \hat{k}$ and $7\hat{i} - 3\hat{j} + 17\hat{k}$ are perpendicular vectors,then what is the value of $a$?

If the non-zero vectors $a$ and $b$ are perpendicular to each other,then the solution of the equation $r \times a = b$ is given by