Q. Let $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}$ are non-collinear vectors. If there exists scalars $\alpha,\beta$ such that $\alpha\overrightarrow{\mathbf{a}} + \beta\overrightarrow{\mathbf{b}} = \overrightarrow{\mathbf{0}}$, then
A) $\alpha = \beta \neq 0$
B) $\alpha + \beta = 0$
C) $\alpha = \beta = 0$
D) $\alpha \neq \beta$
Explanation
(c)
If $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ are non-zero and non-collinear vectors and there exists $\alpha\ and\ \beta$ such that $\alpha\overrightarrow{\mathbf{a}} + \beta\overrightarrow{\mathbf{b}} = \overrightarrow{\mathbf{0}},$ then $\alpha = \beta = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.