Question

a,b,c are three unit vectors such that a+b+c=0, find the value of a.b+b.c+c.a?

Answer 1

seems like it is\[|a||b|\cos(120^{\circ}) + |b||c|\cos(120^{\circ}) + |c||a|\cos(120^{\circ})\]

Answer 2

\[|a|= |b| = |c| = 1\]

Answer 3

also, by the triangle law of addition, since we have \(\vec a + \vec b + \vec c = 0 \), we have this thing:

Answer 4

this is an equilateral triangle, since all the three sides are 1. thus, the three angles are 60, 60, 60. thus, the angles between the vectors are 120, 120, 120.

Answer 5

Oh ok thank k very much..