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

If $\vec{a} = 7\hat{j} + 10\hat{k}$, $\vec{b} = -\hat{i} + 6\hat{j} + 6\hat{k}$ and $\vec{c} = -4\hat{i} + 9\hat{j} + 6\hat{k}$ are the position vectors of the vertices $A, B$ and $C$ respectively of $\triangle ABC$. Then the position vector of the point where the bisector of the angle $A$ meets side $BC$ is

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

If $\vec{a}=\vec{b}+\vec{c},$ then is it true that $|\vec{a}|=|\vec{b}|+|\vec{c}|$ ? Justify your answer.

If $a$ and $b$ are non-collinear vectors and $r$ is a vector coplanar with $a$ and $b$,then ......

Write down a unit vector in the $XY$-plane,making an angle of $30^{\circ}$ with the positive direction of the $x$-axis.