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Scalar Or Dot Product — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSScalar Or Dot Product2 Marks
Question
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are mutually perpendicular unit vectors, write the value of $\big|\vec{\text{a}}+\vec{\text{b}}\big|.$
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Answer

$\vec{\text{a}}$ and $\vec{\text{b}}$ are unit vectors and they are perpendicular.
$\Rightarrow|\vec{\text{a}}|=\big|\vec{\text{b}}\big|=1;\vec{\text{a}}.\vec{\text{b}}=0\dots(1)$
Now,
$\big|\vec{\text{a}}+\vec{\text{b}}\big|^2=|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2+2\vec{\text{a}}.\vec{\text{b}}$
$=1+1+2(0)$ [using (1)]
$=2$
$\therefore\big|\vec{\text{a}}+\vec{\text{b}}\big|=\sqrt{20}$

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