# If two vectors of unequal magnitude are combined, can they give zero resultant?

No. Let $P$ and $Q$ be two vectors and $\theta$ be the angle between them. Then, the resultant $R$ of those two vectors is given by,

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

Thus, the maximum value of $R$ is $P+Q$ at $\theta=0°$. And, the minimum value of $R$ is $P-Q$ at $\theta=180°$. Since the two vectors are unequal $(P≠Q)$, $R$ cannot be equal to zero.