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Question

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

A
√2
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B
√3
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C
1/√2
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D
√5
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Solution

The correct option is B √3

Let ^n1 and ^n2 are the two unit vectors, then the sum is
ns = ^n1 + ^n2 or ns2 = n12 + n22 + 2n1n2cosθ
= 1 + 1 + 2cosθ
Since it is given that ns is also a unit vector, therefore 1 = 1+ 1 + 2 cos θ = cos θ = - 12 θ = 120
Now the difference vector is ^nd = ^n1 - ^n2 or n12 + n22 - 2n1n2cosθ = 1 + 1 - 2 cos(120)
nd2 = 2 - 2(- 12) = 2 + 1 = 3 nd = 3


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