If the position vectors of three points are $a$,$b$,and $(3a - 2b)$,then these points are .....

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

$A$ vector $\vec{a}$ has components $2p$ and $1$ with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise sense. If,with respect to the new system,$\vec{a}$ has components $p+1$ and $1$,then:

If the vectors $2 \hat{i}-3 \hat{j}+6 \hat{k}$ and $\vec{b}$ are collinear and $|\vec{b}|=14$,then $\vec{b}$ has the value

Let $\bar{a}$ and $\bar{b}$ be the position vectors of points $A$ and $B$ respectively. $C$ and $D$ are points on the line $AB$ such that $\overline{AC} = 3 \overline{AB}$ and $\overline{BD} = 2 \overline{BA}$. Find the vector $\overline{CD}$.

If the position vectors of the vertices of a triangle are $6i + 4j + 5k$,$4i + 5j + 6k$,and $5i + 6j + 4k$,then the triangle is