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

If the position vectors of $P$ and $Q$ are $(i + 3j - 7k)$ and $(5i - 2j + 4k)$,then $|\overrightarrow{PQ}|$ is

If $p = 7i - 2j + 3k$ and $q = 3i + j + 5k$,then $|p - 2q| = \dots$

$A$ vector $\vec{a}$ has components $2p$ and $1$ with respect to a rectangular Cartesian system. The system is rotated through a certain angle about the origin in the anti-clockwise sense. If $\vec{a}$ has components $p+1$ and $1$ with respect to the new system,then:

If $\vec{a} = 7\hat{j} + 10\hat{k}$, $\vec{b} = -\hat{i} + 6\hat{j} + 6\hat{k}$ and $\vec{c} = -4\hat{i} + 9\hat{j} + 6\hat{k}$ are the position vectors of the vertices $A, B$ and $C$ respectively of $\triangle ABC$. Then the position vector of the point where the bisector of the angle $A$ meets side $BC$ is

In the given figure,which of the vectors are collinear?