When two velocities $3 {\mathrm{cms}}^{-1}$ and $5 {\mathrm{cms}}^{-1}$ are imposed simultaneously on a body, the body moves with a resultant velocity of $7 {\mathrm{cms}}^{-1}$. What is the angle between the component velocities ?

Two vectors of magnitude $2P$ and $P$ are inclined to each other at a certain angle. If the first vector is doubled, then the resultant vector is increased three times. Calculate the angle between the two vectors.