If the sum of two unit vectors is an unit vector, the magnitude of their difference is

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$\sqrt{2}$

$\sqrt{3}$

$\sqrt{5}$

answer is B.

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Detailed Solution

$|a| = 1 = |b| |a + b| = 1 {|a + b|}^{2} = 1 \Rightarrow 1 + 1 + 2 a . b = 1 \Rightarrow a . b = \frac{- 1}{2} {|a - b|}^{2} = 1 + 1 - 2 a . b = 2 - (- 1) = 3 |a - b| = \sqrt{3}$

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