If vector $a$ has magnitude $5$ and points north-east,and vector $b$ has magnitude $5$ and points north-west,then $|a - b| = $

If $a$ and $b$ are two unit vectors and $\theta$ is the angle between them,then the unit vector along the angular bisector of $a$ and $b$ is given by

Show that the vectors $2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}$ and $3 \hat{i}-4 \hat{j}-4 \hat{k}$ form the vertices of a right-angled triangle.

If $\overrightarrow{a}=\hat{i}+3 \hat{j}+13 \hat{k}$ and $\overrightarrow{b}=2 \hat{i}-4 \hat{j}+3 \hat{k}$ are two vectors,then the component vector of $\vec{a}$ perpendicular to $\vec{b}$ is

If $a, b, c$ are unit vectors satisfying the relation $a+b+\sqrt{3} c=0$,then the angle between $a$ and $b$ is

If three consecutive vertices of a parallelogram are $A(4,3,5)$,$B(0,6,0)$,$C(-8,1,4)$ and $D$ is the fourth vertex,then the angle between $AC$ and $BD$ is