Let a =4 i +3 j and b =3 i +4 j . (a) Find the magnitudes of: 1. … - Vidyadip

Question

Let $\vec{\text{a}}=4\vec{\text{i}}+3\vec{\text{j}}$ and $\vec{\text{b}}=3\vec{\text{i}}+4\vec{\text{j}}. (a)$ Find the magnitudes of:

$\vec{\text{a}}$
$\vec{\text{b}}$
$\vec{\text{a}}+\vec{\text{b}}$
$\vec{\text{a}}-\vec{\text{b}}$

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Answer

$\vec{\text{a}}=4\vec{\text{i}}+3\vec{\text{j}},\vec{\text{b}}=3\vec{\text{i}}+4\vec{\text{j}}$

$|\vec{\text{a}}|=\sqrt{4^2+3^3}=5$
$|\vec{\text{b}}|=\sqrt{9+16}=5$
$|\vec{\text{a}}+\vec{\text{b}}|=|7\vec{\text{i}}+7\vec{\text{j}}|=7\sqrt{2}$
$\vec{\text{a}}-\vec{\text{b}}=(-3+4)\hat{\text{i}}+(-4+3)\hat{\text{j}}=\hat{\text{i}}-\hat{\text{j}}$

$|\vec{\text{a}}-\vec{\text{b}}|=\sqrt{1^2+(-1)^2}=\sqrt{2}.$

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