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If $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7$, then the angle between $\vec{a}$ and $\vec{b}$ is
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Verified Answer
The correct answer is:
$\frac{\pi}{3}$
$\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$
Possible if $\vec{a}, \vec{b}, \vec{c}$ represents sides of a triangle
$\begin{aligned}
& |\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7 \\
& \cos \theta=\frac{a^2+b^2-c^2}{2 a b}=\frac{9+25-49}{2 \times 3 \times 5} \\
& \cos \theta=\frac{-1}{2} \Rightarrow \theta=120=\frac{2 \pi}{3}
\end{aligned}$
$\therefore$ angle between $\vec{a} \& \vec{b}=(\pi-\theta)=\pi-\frac{2 \pi}{3}=\pi / 3$
Possible if $\vec{a}, \vec{b}, \vec{c}$ represents sides of a triangle
$\begin{aligned}
& |\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7 \\
& \cos \theta=\frac{a^2+b^2-c^2}{2 a b}=\frac{9+25-49}{2 \times 3 \times 5} \\
& \cos \theta=\frac{-1}{2} \Rightarrow \theta=120=\frac{2 \pi}{3}
\end{aligned}$
$\therefore$ angle between $\vec{a} \& \vec{b}=(\pi-\theta)=\pi-\frac{2 \pi}{3}=\pi / 3$
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