The projection of a vector $\vec{r} = 3\hat{i} + \hat{j} + 2\hat{k}$ on the $xy$-plane has magnitude:

$A$ vector in the $x-y$ plane makes an angle of $30^{\circ}$ with the $y$-axis. The magnitude of the $y$-component of the vector is $2 \sqrt{3}$. The magnitude of the $x$-component of the vector will be:

If two forces of $5 \, N$ each are acting along $X$ and $Y$ axes,then the magnitude and direction of the resultant is

The $x$-component of the resultant of several vectors is:

Can the magnitude of the rectangular components of a vector be greater than the magnitude of the vector itself? Explain.

One of the rectangular components of a force of $40 \ N$ is $20 \sqrt{3} \ N$. What is the other rectangular component (in $N$)?