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Q.

If the sum of two unit vectors is also a vector of unit magnitude, the magnitude of the difference of the two unit vectors is

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a

1 unit

b

2 units

c

$\sqrt{3} units$

d

zero

answer is C.

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Detailed Solution

$P = 1; Q = 1; R = 1$

$1 = 1^{2} + 1^{2} + 2 \times 1 \times 1 \times \cos θ$

$1 = 2 + 2 \cos θ$

$\cos θ = \frac{- 1}{2}$

$R = \sqrt{1^{2} + 1^{2} - 2 (1) (1) \cos θ}$

$R = \sqrt{1 + 1 + 2 (1) (1) \frac{1}{2}}$

$R = \sqrt{3}$

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If the sum of two unit vectors is also a vector of unit magnitude, the magnitude of the difference of the two unit vectors is