If $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors,then the greatest value of $\sqrt{3}|\overrightarrow{a}+\overrightarrow{b}|+|\overrightarrow{a}-\overrightarrow{b}|$ is

Let $u$ and $v$ be two non-zero vectors. If $|u+v|=|u-v|$,then:

If $|a| = 3$,$|b| = 4$ and the angle between $a$ and $b$ is $120^\circ$,then $|4a + 3b| = $

If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are three vectors such that $\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}$ and the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\frac{\pi}{2}$, then:

$ABCD$ is a parallelogram and $P$ is a point on the segment $AD$ dividing it internally in the ratio $3:1$. If the line $BP$ meets the diagonal $AC$ in $Q$, then $AQ:QC$ equals

If $\vec{a}$ is perpendicular to $\vec{b}$ and $\vec{r}$ is a non-zero vector such that $p\vec{r} + (\vec{r} \cdot \vec{b})\vec{a} = \vec{c}$,then $\vec{r} = $