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

MCQ

If $a, b $ and $c $ are unit vectors such that $a + b - c = 0,$ then the angle between $a$ and $b$ is

A
$\pi /6$
B
$\pi /3$
C
$\pi /2$
✓
$2\pi /3$

✓

Answer

Correct option: D.

$2\pi /3$

d
(d) Given condition is $a + b = c.$

Using dot product, $(a + b).(a + b) = c.c$

$ \Rightarrow a.a + b.b + 2a.b = c.c$

$ \Rightarrow \,|a|.|a|\cos 0^\circ + |b|.|b|\cos 0^\circ + 2|a|.|b|\cos \alpha $

$ = \,|c|.|c|\cos 0^\circ $, $(\because \,\,\,|a|\, = \,|b|\, = \,|c|\, = 1)$

$ \Rightarrow 1 + 1 + 2\cos \alpha = 1 \Rightarrow \cos \alpha = - \frac{1}{2} \Rightarrow \alpha = \frac{{2\pi }}{3}$.

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