Q. If $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}$ are two non-collinear vectors and $x\ \overrightarrow{\mathbf{a}} + y\ \overrightarrow{\mathbf{b}} = 0$
A) $x = 0,$ but $y$ is not necessarily zero
B) $y = 0$, but $x$ is not necessarily zero
C) $x = 0,\ y = 0$
D) None of the above
Explanation
(c)
If $\overrightarrow{\mathbf{a}}\mathbf{,}\overrightarrow{\mathbf{b}}$ are two non-zero non-collinear vectors and $x,y$ are two scalars such that $x\overrightarrow{\mathbf{a}} + y\overrightarrow{\mathbf{b}} = 0,\ then\ x = 0,\ y = 0$.
Because otherwise one will be a scalar multiple of the other and hence collinear, which is a contradiction
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.