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Scalar Or Dot Product — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product1 Mark
MCQ
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:
  • A
    $\lambda=1$
  • B
    $\lambda=-1$
  • C
    $\text{a}=|\lambda|$
  • ✓
    $\text{a}=\frac{1}{|\lambda|}$
✓

Answer

Correct option: D.
$\text{a}=\frac{1}{|\lambda|}$
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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