If the coordinates of points $A, B, C,$ and $D$ are $(1, 2, 3), (4, 5, 7), (-4, 3, -6),$ and $(2, 9, 2)$ respectively,then the angle between $AB$ and $CD$ is:

Let $a = i$ be a vector which makes an angle of $120^\circ$ with a unit vector $b$. Then the unit vector $(a + b)$ is

$A$ force is a

The direction of the vectors $(1, 1, 2)$ and $(2, 1, 0)$ is $.......$

Let $\hat{i}-\hat{j}+2 \hat{k}$ and $\hat{i}+2 \hat{j}-2 \hat{k}$ be the position vectors of points $A$ and $B$ respectively. If $C$ is a point on the line joining $A$ and $B$ such that $BC=10$,then the position vector of $C$ can be

If $a, b, c$ are three non-coplanar vectors such that $a + b + c = \alpha d$ and $b + c + d = \beta a$,then $a + b + c + d$ is equal to