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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 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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