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Question

The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vectors is?


A

3

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B

1-3

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C

1+3

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D

-3

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Solution

The correct option is A

3


Explanation for the correct option:

Let a,b be two unit vectors and the summation of these two unit vectors be equal to c which is also a unit vector. Thus,

a+b=c

by squaring both sides,

a+b2=c2a2+b2+a·b+a·b=c2

Since, a=b=c=1

1+1+2a·b=12a·b=-1

a-b2=a2+b2-2aba-b2=1+1-(-1)a-b2=3a-b=3

Hence, option (A) is correct.


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