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

$A$ vector of magnitude $14$ lies in the $xy-$ plane and makes an angle of $60^\circ$ with the $x-$ axis. The components of the vector in the direction of the $x-$ axis and $y-$ axis are:

$P$ is the point of intersection of the diagonals of the parallelogram $ABCD$. If $S$ is any point in space and $\vec{SA} + \vec{SB} + \vec{SC} + \vec{SD} = \lambda \vec{SP}$, then $\lambda$ equals

The points with position vectors $10\,i + 3\,j$,$12\,i - 5\,j$,and $a\,i + 11\,j$ are collinear,if $a = $

If $a = 2i + j - 8k$ and $b = i + 3j - 4k,$ then the magnitude of $a + b = $

If the position vectors of three points are $a$,$b$,and $(3a - 2b)$,then these points are .....