If $a = 2i + 2j - k$ and $|xa| = 1$,then $x =$

In a regular hexagon $ABCDEF$,$\overrightarrow{AE} = $

If $\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}$ and $\vec{b}=2 \hat{i}-3 \hat{j}-5 \hat{k}$,then

If $C$ is the midpoint of $AB$ and $P$ is any point outside $AB$,then

$(3, 0, 2)$ and $(0, 2, k)$ are the direction ratios of two lines and $\theta$ is the angle between them. If $|\cos \theta| = \frac{6}{13}$, then $k =$

Find the unit vector in the direction of vector $\overrightarrow{PQ},$ where $P$ and $Q$ are the points $(1, 2, 3)$ and $(4, 5, 6),$ respectively.