If $\overrightarrow{a} \cdot \overrightarrow{b} = -|\overrightarrow{a}||\overrightarrow{b}|$,then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is (in $^{\circ}$)

$A$ particle acted on by constant forces $4i + j - 3k$ and $3i + j - k$ is displaced from the point $i + 2j + 3k$ to the point $5i + 4j + k$. The total work done by the force is ............... $unit$.

If $\vec{a}, \vec{b}$ and $\vec{c}$ are unit vectors such that $\vec{a}$ is perpendicular to $\vec{b}$ and $\vec{c}$,and $|\vec{a} + \vec{b} + \vec{c}| = 1$,then the angle between $\vec{b}$ and $\vec{c}$ is:

If $a \perp b$ and $(a+b) \perp (a+mb)$,then $m$ is equal to

The angle between the diagonals of the parallelogram whose adjacent sides are $2 \hat{i}+4 \hat{j}-5 \hat{k}$ and $\hat{i}+2 \hat{j}+3 \hat{k}$ is

If $a = 2i + 2j + 3k$,$b = -i + 2j + k$,and $c = 3i + j$,then $a + tb$ is perpendicular to $c$ if $t = $