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Question

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

A
2units
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B
2 units
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C
3units
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D
5units
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Solution

The correct option is D 3units
Let a,b be two unit vectors whose sum is also a unit vector c

a+b=c ...... (i) and |a|=|b|=|c|=1

Now, magnitude of sum of a and b is

|a+b|=|a|2+|b|2+2(ab)

1=1+1+2(ab) ..... From (i)

ab=12

Magnitude of their difference is given by

|ab|2=|a|2+|b|22a.b

=1+1+2×12=3

|ab|=3

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