If a, b, c are unit vectors such that a + b + c = 0, then a , ,. … - Vidyadip

MCQ

If $a, b, c $ are unit vectors such that $a + b + c = 0,$ then $a\,\,.\,\,b + b\,\,.\,\,c + c\,\,.\,\,a = $

A
$1$
B
$3$
✓
$-3/2$
D
$3/2$

✓

Answer

Correct option: C.

$-3/2$

c
(c) Squaring $(a + b + c) = 0,$

we get ${a^2} + {b^2} + {c^2} + 2a.b + 2b.c + 2c.a = 0$

==> $|a{|^2} + |b{|^2} + |c{|^2} + 2(a.b + b.c + c.a) = 0$

==> $2(a.b + b.c + c.a) = - 3$ $ \Rightarrow a.b + b.c + c.a = - \frac{3}{2}$.

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