If the position vectors of the vertices $A, B, C$ of a triangle $ABC$ are $7j + 10k$,$-i + 6j + 6k$,and $-4i + 9j + 6k$ respectively,then the triangle is:

The position vectors of the points $P$ and $Q$ are respectively $-2 \bar{i}-3 \bar{j}+\bar{k}$ and $3 \bar{i}+3 \bar{j}+2 \bar{k}$. The ratio in which the point having position vector $\frac{-9}{2} \bar{i}-6 \bar{j}+\frac{1}{2} \bar{k}$ divides the line segment joining $P$ and $Q$ is

Show that the points $A (-2 \hat{i}+3 \hat{j}+5 \hat{k})$,$B (\hat{i}+2 \hat{j}+3 \hat{k})$ and $C (7 \hat{i}-\hat{k})$ are collinear.

If the position vectors of the points $A, B, C$ are $a, b, 3a - 2b$ respectively,then the points $A, B, C$ are

Let $ABCDEF$ be a regular hexagon with the vertices $A, B, C, D, E, F$ in counterclockwise order. Then the vector $\vec{AB} + \vec{AF} + \vec{CD} + \vec{EF}$ is equal to

For three vectors $p, q$ and $r$,if $r = 3p + 4q$ and $2r = p - 3q$,then