If $a$ and $b$ are two vectors such that $a \cdot b = 0$ and $a \times b = 0$,then .....

If $A, B, C, D$ are any four points and $E$ and $F$ are the midpoints of $AC$ and $BD$ respectively,then $\overline{AB} + \overline{CB} + \overline{CD} + \overline{AD} = \dots$

If $\vec{PO} + \vec{OQ} = \vec{QO} + \vec{OR}$,then

If $\vec{a} = \langle \frac{1}{3}, \frac{1}{3}, \frac{1}{3} \rangle$,then what is its magnitude?

If in a triangle $\overrightarrow{AB} = \vec{a}$ and $\overrightarrow{AC} = \vec{b}$,and $D$ and $E$ are the mid-points of $AB$ and $AC$ respectively,then $\overrightarrow{DE}$ is equal to:

Let $O$ be the origin, $\vec{OP} = \vec{a}$ and $\vec{OQ} = \vec{b}$. If $R$ is the point on $\vec{OP}$ such that $\vec{OP} = 5\vec{OR}$, and $M$ is the point such that $\vec{OQ} = 5\vec{RM}$, then $\vec{PM}$ is equal to: