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Question

If the sum of two unit vectors is a unit Vector, then find the magnitude of difference.

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Solution

Let a & b be two unit vector.
Then the resultant sum of two vector is given by |a|=b=1
a+b=|a|2+b2+2|a|bcosθ
it given a+b=1
1=1+1+2cosθ
cosθ=1/2
θ=1200
ab=|a|2+b22|a|bcosθ
=1+12×(12)
ab=3

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