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 the above

Answer 1

The correct option is C $x=0,y=0$

We are given that a and b are non-collinear vectors.

In addition, $x\overline{a}+y\overline{b}=0$

Rearranging$x\overline{a}=-y\overline{b}$

let$k=\frac{y}{x}$

$\Rightarrow \overline{a}=-k\overline{b}$

This tells us a and b should be collinear but that contradicts the given statement.

Thus the only solution plausible is $\overline{a}=0and\overline{b}=0,$ that is both are zero vectors.