Question

If $a$ and $b$ be two perpendicular unit vectors such that $x=b-(a\times x)$, then $\left|x\right|$ is equal to

• A. $1$
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\sqrt{3}$

Answer 1

The correct option is B $\sqrt{2}$

We have
$a.x=0$
Also, $x=b+(x\times a)$
$\Rightarrow x\times a=b\times a+(x\times a)\times a$
$\Rightarrow x\times a=b\times a+(x.a)a-(a.a)x$
$\Rightarrow x-b=b\times a-x$
$\left|2x\right|=|b+b\times a|$
$\Rightarrow \left|x\right|=\frac{1}{\sqrt{2}}$