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Question

Let a and b be two unit vectors such that a+b is also a unit vector. Then the angle between a and b is

A
π6
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B
π3
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C
π2
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D
2π3
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Solution

The correct option is D 2π3
a and b are unit vectors.
|a|=|b|=1
Also, a+b is a unit vector.
|a+b|2=1
|a|2+|b|2+2ab=1
12+12+2×1×1×cosθ=1
cosθ=12
θ=2π3

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