In a parallelogram $ABCD$,if the diagonals are $\overline{AC}$ and $\overline{BD}$,then $\overline{AC} - \overline{BD} = \dots$

If $\vec{a} = \hat{i}+\hat{j}-\hat{k}$ and $\vec{b} = 2\hat{i}-3\hat{j}+\hat{k}$ are adjacent sides of a parallelogram,then the lengths of its diagonals are

In a parallelogram $ABCD$,if $\vec{AC}$ and $\vec{BD}$ are the diagonals,then which of the following is equal to $\vec{AC} + \vec{BD}$?

If the vector $a = 2 \hat{i} + 3 \hat{j} + 6 \hat{k}$ and $b$ are collinear and $|b| = 21$, then $b$ is equal to:

Find the vector $\vec{c}$ which is in the direction of the internal angle bisector of the vectors $\vec{a} = 7\hat{i} - 4\hat{j} - 4\hat{k}$ and $\vec{b} = -2\hat{i} - \hat{j} + 2\hat{k}$ with $|\vec{c}| = 5\sqrt{6}$.

If $\vec{a} = \langle \frac{1}{3}, \frac{1}{3}, \frac{1}{3} \rangle$,then what is its magnitude?