The magnitude of the projection of the vector $\vec{a} = -\hat{i} + 2\hat{j} - \hat{k}$ on the unit vector $\hat{i}$ is . . . . . . .

If $|a| = 3, |b| = 4$ and $|a + b| = 5,$ then $|a - b| = $

$A$ vector of magnitude $\sqrt{2}$ units along the internal bisector of the angle between the vectors $\vec{a} = 2 \hat{i} - 2 \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2 \hat{j} + 2 \hat{k}$ is

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

For three vectors $p, q$ and $r$,if $r = 3p + 4q$ and $2r = p - 3q$,then

$A$ vector in the direction of $v = 2\hat{i} + 3\hat{j} + \hat{k}$ with magnitude $\sqrt{7}$ is