If a is a nonzero vector of magnitude ^ a^ and a nonzero scalar, … - Vidyadip

MCQ

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

A
$\lambda=1$
✓
$a=\frac{1}{|\lambda|}$
C
$a =|\lambda|$
D
$\lambda=-1$

✓

Answer

Correct option: B.

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

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

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

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

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

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

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

The correct answer is $B$

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