If $\vec{a}+\vec{b}+\vec{c}=0, |\vec{a}|=3, |\vec{b}|=5,|\vec{c}|=7$ then the angle between $\vec{a}$ and $\vec{b}$ is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{\pi}{3}$
$\vec{a}+\vec{b}+\vec{c}=0$
$\vec{a}+\vec{b}=-\vec{c}$ squaring both sides
$(\vec{a}+\vec{b}).(\vec{a}+\vec{b})=|\vec c|^2$
$|\vec{a}|^2+|\vec{b}|^2+\vec{a}.\vec{b}=|\vec{c}|^2$
$9+25+2|\vec{a}||\vec{b}|\cos θ=49$ θ → angle between a and b
$2×3×5\cos θ=15$
$\cos θ=\frac{1}{2}⇒θ=\frac{\pi}{3}$