Find the values of $x$ and $y$ so that the vectors $2 \hat{i} + 3 \hat{j}$ and $x \hat{i} + y \hat{j}$ are equal.

In the figure,a vector $x$ satisfies the equation $x - w = v$. Then $x =$

If $C$ is the midpoint of $\overline{AB}$ and $P$ is any point not on $\overline{AB}$,then which of the following is true?

The direction cosines of the vector $\hat{i}-2\hat{j}+3\hat{k}$ are . . . . . . .

$P$ is the point of intersection of the diagonals of the parallelogram $ABCD$. If $O$ is any point,then $\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC} + \overrightarrow{OD} = $

If $\bar{a} = \hat{i} + \hat{j} + \hat{k}$,$\bar{b} = 4\hat{i} - 2\hat{j} + 3\hat{k}$,and $\bar{c} = \hat{i} - 2\hat{j} + \hat{k}$,then the vector of magnitude $6$ units,which is parallel to the vector $2\bar{a} - \bar{b} + 3\bar{c}$,is: