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Model Paper 4 — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSModel Paper 43 Marks
Question
Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three vectors such that $|\vec{a}|=3,|\vec{b}|=4,|\vec{c}|=5$ and each one of them being $\perp$ to the sum of the other two, find $|\vec{a}+\vec{b}+\vec{c}|$
✓

Answer

$\vec{a} \cdot(\vec{b}+\vec{c})=0, \vec{b} \cdot(\vec{c}+\vec{a})=0, \vec{c} \cdot(\vec{a}+\vec{b})=0$
$($Given$) |\vec{a}+\vec{b}+\vec{c}|^2=(\vec{a}+\vec{b}+\vec{c}) \cdot(\vec{a}+\vec{b}+\vec{c})$
$=\vec{a} \cdot \vec{a}+\vec{a} \cdot(\vec{b}+\vec{c})+\vec{b} \cdot \vec{b}+\vec{b} \cdot(\vec{a}+\vec{c})+\vec{c} \cdot \vec{c}+\vec{c} \cdot(\vec{a}+\vec{b})$
$=|\vec{a}|^2+|\vec{b}|^2+|\vec{c}|^2$
$=9+16+25$
$=50$
$|\vec{a}+\vec{b}+\vec{c}|=\sqrt{50}$
$=5 \sqrt{2}$

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