Question

A vector v is called a unit vector if ||v||=1.

Let a,b, and c be unit vectors, such that a+b+c = 0. Show that the angle between any two of these vectors is \(120^{\circ}\).

Answer 1

look at

\[a\cdot(a+b+c = 0)\]
\[b\cdot(a+b+c = 0)\]
\[c\cdot(a+b+c = 0)\]