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Algebra of Vectors — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAlgebra of Vectors1 Mark
Question
If $\vec{\text{a}}$ ia a non-zero vector of modulus a and m is a non-zero scalar such that $\text{m}\vec{\text{a}}$ is the unit vector, write the value of m.
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Answer

Given $\vec{\text{a}}$ is a non-zero vector of modulus a. Also, $\text{m}\vec{\text{a}}$ is the unit vector. Therefore,$|\text{m}\vec{\text{a}}|=1$
$\Rightarrow\ |\text{m}||\vec{\text{a}}|=1$
$\Rightarrow\ |\text{m}|\text{a}=1$
$\Rightarrow\ |\text{m}|=\frac{1}{\text{a}}$
$\Rightarrow\ \text{m}=\pm\frac{1}{\text{a}}$

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