# Can the resultant magnitude of two vectors be smaller than the magnitude of either vector?

Yes. Let $P$ and $Q$ be two vectors acting at an angle of $\theta$. Then, the resultant $R$ of the two vectors is,

$R=\sqrt{P^2+Q^2+2PQ\cos\theta}$

The minimum value of $R$ is $P-Q$ at an angle $180°$.

Hence, depending on the values of $P$ and $Q$, the value of $R$ can be smaller than either $P$ or $Q$.