If vector a , b and c are such that a + b + c =0 and | a |=3, | b… - Vidyadip

Question

If vector $\vec{\text{a}},\vec{\text{b}}\text{ and }\vec{\text{c}}$ are such that $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}=0\text{ and }|\vec{\text{a}}|=3, |\vec{\text{b}}|=5\text{ and }|\vec{\text{c}}|=7$ find the angle between $ \vec{\text{a}}$and $ \vec{\text{b}}$.

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Answer

$\vec{\text{a}}+\vec{\text{b}}=-\vec{\text{c}}$
$|\vec{\text{a}}|^{2}+|\vec{\text{b}}|^{2}+2\vec{\text{ a}}\cdot\vec{\text{b}}=|\vec{\text{c}}|^{2}$
$9+25+2\text{ }|\vec{\text{a}}|\text{ }|\vec{\text{b}}|\cos\theta=49$
$30\cos\theta=15\Rightarrow\cos\theta=\frac{1}{2}\Rightarrow\theta=60^{o}=\frac{\pi}{3}.$

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