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Scalar Or Dot Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product2 Marks
Question
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors such that $\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big).=0,$ find the relation betwen the magnitudes of $\vec{\text{a}}$ and $\vec{\text{b}}.$
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Answer

Given that$\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big)=0$
$\Rightarrow|\vec{\text{a}}|^2-\big|\vec{\text{b}}\big|^2=0$
$\Rightarrow|\vec{\text{a}}|^2=\big|\vec{\text{b}}\big|^2$
$\therefore|\vec{\text{a}}|=\big|\vec{\text{b}}\big|$

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