Let | a | = | b | = | a - b | = ,1 then angle between a and b is - Vidyadip

MCQ

Let $\left| {\vec a} \right| = \left| {\vec b} \right| = \left| {\vec a - \vec b} \right| = \,1$ then angle between $\vec a$ and $\vec b$ is

A
$\frac{\pi }{6}$
✓
$\frac{\pi }{3}$
C
$\frac{\pi }{4}$
D
$\frac{\pi }{2}$

✓

Answer

Correct option: B.

$\frac{\pi }{3}$

b
$|\overrightarrow a - \overrightarrow b {|^2} = 1$

$ \Rightarrow |\vec a{|^2} + |\vec b{|^2} - 2\left| {\vec a} \right|\left| {\vec b} \right|\cos \theta = 1$

$ \Rightarrow \cos \theta=1 / 2 \Rightarrow \cos \theta=1 / 2 $

$\Rightarrow \theta=\pi / 3$

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