# 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.

• mod is not used for the modulus. You should use $\|\cdot \|$ or $|\cdot |$ instead. For the question itself, it is just a matter of applying the en.wikipedia.org/wiki/Law_of_cosines, as the condition is telling you that the three vectors form a triangle (this you need to understand) Jun 30 '16 at 5:49
• Going off b00n h3T's comment: $|c|^2 = |a|^2 + |b|^2 - 2|a||b|cos(\theta)$. Solving for $\theta$ will give you the angle between $a$ and $b$. Jun 30 '16 at 5:56
• @Sentient actually that will give you the "nose to tail" angle. The exterior angle (which is supplementary to that) corresponds to the angle between $a$ and $b$ from a common origin. Jun 30 '16 at 6:29