Classify the following measure as a scalar or a vector:
$1000 \, cm^{3}$

Find the values of $x, y$ and $z$ so that the vectors $\vec{a} = x \hat{i} + 2 \hat{j} + z \hat{k}$ and $\vec{b} = 2 \hat{i} + y \hat{j} + \hat{k}$ are equal.

If the position vectors of points $P, Q, R,$ and $S$ are $2\hat{i} + 3\hat{j} + 5\hat{k}$,$\hat{i} + 2\hat{j} + 3\hat{k}$,$-5\hat{i} + 4\hat{j} - 2\hat{k}$,and $\hat{i} + 10\hat{j} + 10\hat{k}$ respectively,then:

The angle made by the position vector of the point $(5, -4, -3)$ with the positive direction of the $X$-axis is:

What should be added to the vector $a = 3i + 4j - 2k$ to obtain the resultant vector $i$?

Write down a unit vector in the $XY$-plane,making an angle of $30^{\circ}$ with the positive direction of the $x$-axis.