If $a = 2i + 5j$ and $b = 2i - j,$ then the unit vector along $a + b$ will be

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

The vertices of triangle $ABC$ are $A \equiv (3, 0, 0)$,$B \equiv (0, 0, 4)$,and $C \equiv (0, 5, 4)$. Find the position vector of the point $D$ where the angle bisector of $\angle A$ meets $BC$.

If two vertices of a triangle are $\hat{i} - \hat{j}$ and $\hat{j} + \hat{k}$,then the third vertex can be

$A$ vector coplanar with the non-collinear vectors $\vec{a}$ and $\vec{b}$ is:

If $D, E, F$ are the midpoints of the sides $BC, CA$ and $AB$ of the triangle $ABC$,then $\overrightarrow{AD} + \overrightarrow{BE} + \overrightarrow{CF}$ is: