Two unit vectors when added give a unit vector. Then, choose the correct statement.

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Magnitude of their difference is 1

Magnitude of their difference is $\sqrt{3}$

Angle between the sum and the difference of the two vectors is 90°

Angle between the vectors is 90°

answer is A, D.

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Detailed Solution

From $R = \sqrt{A^{2} + B^{2} + 2 A B \cos θ}$

We have,

$1 = \sqrt{1 + 1 + 2 \cos θ} o r \cos θ = - \frac{1}{2} ∴ θ = 120 °$

$S = \sqrt{A^{2} + B^{2} - 2 A B \cos θ} = \sqrt{1 + 1 - 2 \times 1 \times 1 \times (- \frac{1}{2})} = \sqrt{3} (\hat{a_{1}} + \hat{a_{2}}) . ({\hat{a}}_{1} - {\hat{a}}_{2}) = 0$

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