If the position vector of one end of a line segment $AB$ is $2i + 3j - k$ and the position vector of its midpoint is $3(i + j + k)$,then what is the position vector of the other end?

Statement $(A):$ In $\Delta ABC$,$\overline{AB} + \overline{BC} + \overline{CA} = 0$.
Reason $(R):$ If $\overline{AB} = \vec{a}$ and $\overline{BC} = \vec{b}$,then $\overline{AC} = \vec{a} + \vec{b}$ (Triangle Law of Addition).

$A$ vector $\vec{r}$ has magnitude $14$ and direction ratios $2, 3, -6$. Find the direction cosines and components of $\vec{r}$,given that $\vec{r}$ makes an acute angle with the $x$-axis.

In the given figure,which of the vectors are equal?

Let $\overline{OA}=\overline{a}, \overline{OB}=\overline{b}$. If the vector along the angle bisector of $\angle AOB$ is given by $x \frac{\overline{a}}{|\overline{a}|}+y \frac{\overline{b}}{|\overline{b}|}$,then which of the following is true?

$A$ vector $\vec{r}$ of magnitude $3\sqrt{2}$ units which makes angles of $\pi/4$ and $\pi/2$ respectively with $Y$ and $Z$ axes is: