<s>[INST] finding the angle between two vectors If $a,b$ and $c$ be three vectors such that $|\, a \,|=3$, $|\, b \,|=5$ and $|\, c \,|=7$ and $a+b+c=0$. Then find the angle between $a$ and $b$.
I tried by taking $a=-(b+c)$ and $b=-(c+a)$. But couldn't proceed further. Please help.
 [/INST] \begin{align*}
  \mathbf{a+b+c} &=\mathbf{0} \\
  \mathbf{c} &=-(\mathbf{a+b}) \\
  \mathbf{c}\cdot \mathbf{c} &= (\mathbf{a+b})\cdot (\mathbf{a+b}) \\
  c^2 &= a^2+b^2+2\mathbf{a\cdot b} \\
  2\mathbf{a\cdot b} &= c^2-a^2-b^2 \\
  \cos \theta_{ab} &= \frac{c^2-a^2-b^2}{2ab} \\
  &= \frac{7^2-3^2-5^2}{2(3)(5)} \\
  &= \frac{1}{2} \\
  \theta_{ab} &= 60^{\circ}
\end{align*}
</s>