Find the value of $x$ for which $x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector.

If $p = (7, -2, 3)$ and $q = (3, 1, 5)$,then the magnitude of $p - 2q$ is $......$.

If $\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} - \hat{k}$,then $\vec{a} + \vec{b} = \dots$

The vectors $3i + j - 5k$ and $ai + bj - 15k$ are collinear if $....$

If $a$ and $b$ represent two non-collinear vectors,the equation $r = ta + (1-t)b$ represents

If the position vectors of the points $A$ and $B$ are $2 \hat{i}+3 \hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+2 \hat{k}$ respectively,then the unit vector along $\overrightarrow{BA}$ and in the direction of $\overrightarrow{AB}$ is