$\bar{a}$ and $\bar{b}$ are non-collinear vectors. If $\bar{p} = (2x + 1)\bar{a} - \bar{b}$ and $\bar{q} = (x - 2)\bar{a} + \bar{b}$ are collinear vectors,then $x =$

If $\vec{a}$ and $\vec{b}$ are non-collinear vectors,then the value of $\alpha$ for which the vectors $\vec{u} = (\alpha - 2)\vec{a} + \vec{b}$ and $\vec{v} = (2 + 3\alpha)\vec{a} - 3\vec{b}$ are collinear is:

If $\vec{a}, \vec{b}, \vec{c}$ are $3$ vectors such that $|\vec{a}|=5, |\vec{b}|=8, |\vec{c}|=11$ and $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$,then the angle between the vectors $\vec{a}$ and $\vec{b}$ is

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

If $\vec{a} = \vec{b}$,then............

If the magnitudes of $\bar{a}$,$\bar{b}$ and $\bar{a}+\bar{b}$ are respectively $3$,$4$ and $5$,then the magnitude of $\bar{a}-\bar{b}$ is