# Ifis a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then λis unit vector if

Question:

If $\vec{a}$ is a nonzero vector of magnitude ' $a$ ' and $\lambda$ a nonzero scalar, then $\lambda \vec{a}$ is unit vector if

(A) $\lambda=1$

(B) $\lambda=-1$ (C) $a=|\lambda|$

(D) $a=\frac{1}{|\lambda|}$

Solution:

Vector $\lambda \vec{a}$ is a unit vector if $|\lambda \vec{a}|=1$.

Now,

$|\lambda \vec{a}|=1$

$\Rightarrow|\lambda||\vec{a}|=1$

$\Rightarrow|\vec{a}|=\frac{1}{|\lambda|}$             $[\lambda \neq 0]$

$\Rightarrow a=\frac{1}{|\lambda|}$                       $[|\vec{a}|=a]$

Hence, vector $\lambda \vec{a}$ is a unit vector if $a=\frac{1}{|\lambda|}$.