Classify the following measure as a scalar or a vector:
$20 \text{ m/s}$ towards north

Find the sum of the vectors $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$,$\vec{b}=-2 \hat{i}+4 \hat{j}+5 \hat{k}$,and $\vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}$.

In a triangle $ABC$, if $\overline{BC} = \bar{i} - 2\bar{j} + 2\bar{k}$ and $\overline{CA} = 6\bar{i} + 3\bar{j} - 2\bar{k}$, then the perimeter of the triangle is

Find the position vector of a point $R$ which divides the line joining the two points $P$ and $Q$ with position vectors $\overrightarrow{OP} = 2\vec{a} + \vec{b}$ and $\overrightarrow{OQ} = \vec{a} - 2\vec{b}$ respectively,in the ratio $1:2$,$(i)$ internally and (ii) externally.

If $a = 2i + 2j - k$ and $|xa| = 1$,then $x =$

If the direction cosines of a vector of magnitude $3$ are $\frac{2}{3}, -\frac{1}{3}, \frac{2}{3}$,then the vector is: