$A$ force of $5 \, N$ acts at an angle of $60^\circ$ with the vertical. Find the vertical component of the force in $N$.

Two forces of magnitude $P$ and $Q$ acting at a point have a resultant $R$. The resolved part of $R$ in the direction of $P$ is of magnitude $Q$. The angle between the forces is:

What is the maximum number of components into which a vector can be resolved?

$A$ certain vector in the $xy$-plane has an $x$-component of $4 \,m$ and a $y$-component of $10 \,m$. It is then rotated in the $xy$-plane so that its $x$-component is doubled. Then its new $y$-component is (approximately) (in $\,m$)

$A$ displacement vector of magnitude $4$ makes an angle $30^{\circ}$ with the $x$-axis. Its rectangular components in the $x-y$ plane are .........

Explain the resolution of vectors.