Let $\vec{a}, \vec{b}, \vec{c}$ be three unit vectors such that $\vec{a} . \vec{b}=\vec{a} . \vec{c}=0$ If the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{4}$, then $\vec{a}=\lambda(\vec{b} \times \vec{c})$, where ' $\lambda$ ' is equal to:

± $\sqrt{2}$

$\vec{a}=\lambda(\vec{b} \times \vec{c})$

$\Rightarrow|\vec{a}|=|\lambda||\vec{b} \times \vec{c}|=|\lambda \| \vec{b}||\vec{c}| \sin \frac{\pi}{4}$

$\Rightarrow|\lambda|=\sqrt{2}$

$\Rightarrow|\lambda|= \pm \sqrt{2}$

Hence (2) is correct answer.