NIMCET 2012 Question Paper with solutions

Given, a, b and c are unit vectors.
∴ |a| = |b| = |c| = 1
Now, we have
a + b + c = 0
∴ ${\left|\mathit{a}+\mathit{b}+\mathit{c}\right|}^2$ = 0
⇒ ${\left|\mathit{a}\right|}^2+|\mathit{b}{|}^2+|\mathit{c}{|}^2$ + 2 (a.b + b.c + c.a) = 0
⇒ 1 + 1 + 1 + 2 (a.b + b.c + c.a) = 0
⇒ a.b + b.c + c.a = - $\frac{3}{2}$