# Show that two vectors of different magnitudes cannot be combined to give zero resultant, whereas three vectors can be.

Let $\vec{P}$ and $\vec{Q}$ be two vectors with different magnitudes. Minimum scalar magnitude obtained by combining them is, $|\vec{A}-\vec{B}|>0\;\;\;\text{as}\;\vec{A}≠\vec{B}$

Therefore, two vectors with different magnitudes cannot be combined to give zero resultant.

Three vectors can be combined to give zero resultant as they can be represented by the sides of a triangle taken in order. [Triangle of Forces]