Let $ABC$ be a triangle. Let $u = \vec{AB}$ and $v = \vec{AC}$. If $D$ is the midpoint of $BC$,then $\vec{AD} =$

Let $u$ and $v$ be two vectors in $R^2$. If $|u+v|^2=2(|u|^2+|v|^2)$,then .....

If $M$ and $N$ are the mid-points of the sides $BC$ and $CD$ respectively of a parallelogram $ABCD$, then $AM + AN$ equals

Suppose $ABCDE$ is a pentagon. The resultant vector of the vectors $\vec{AB}, \vec{AE}, \vec{BC}, \vec{DC}, \vec{ED}$ and $\vec{AC}$ is

Let $\vec{a}$ and $\vec{b}$ be two non-collinear vectors. For what values of $x$ and $y$ is the equation $2\vec{u} - \vec{v} = \vec{w}$ true,where $\vec{u} = x\vec{a} + 2y\vec{b}$,$\vec{v} = -2y\vec{a} + 3x\vec{b}$,and $\vec{w} = 4\vec{a} - 2\vec{b}$?

Let $P, Q, R,$ and $S$ be points on a plane with position vectors $-2\hat{i} - \hat{j}$,$4\hat{i}$,$3\hat{i} + 3\hat{j}$,and $-3\hat{i} + 2\hat{j}$ respectively. What type of quadrilateral is $PQRS$?