If a is a non-zero of magnitude 'a' and is a non-zero scalar, the… - Vidyadip

Question

If $\vec{\text{a}}$ is a non-zero of magnitude 'a' and $\lambda$ is a non-zero scalar, then $\lambda\vec{\text{a}}$ is a unit vector if:

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

✓

Answer

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

Solution:

Given that

$|\vec{\text{a}}|=\text{a};$

Now,

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

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

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

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

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