Question

If $a$ and $b$ are two non-collinear vectors and $xa+yb=0$ then:

• 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 these

Answer 1

Answer: (C)

$x=0$, $y=0$

Given that $a$ and $b$ are two non collinear vectors and $ax+by=0$

$\Rightarrow \frac{a}{b}=-\frac{y}{x}$

Given that $a$ and $b$ are non collinear , so $a$ and $b$ should not be parallel , therefore $\frac{y}{x}=0$

$\Rightarrow y=0$

The given equation can also be written as $\frac{b}{a}=-\frac{x}{y}$

Given that $a$ and $b$ are non collinear , so $a$ and $b$ should not be parallel , therefore $\frac{x}{y}=0$

$\Rightarrow x=0$

Therefore option $C$ is correct