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If the sum of two unit vectors is a unit...

If the sum of two unit vectors is a unit vector,then find the magnitude of their differences.

A

`sqrt2`

B

`sqrt3`

C

`(1)/(sqrt2)`

D

`sqrt5`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `hatn_1` and `hat_2` are the two unit vectors, then the sum is
`vecn_S=hatn_1+hatn_2 or n_S^(2)=n_1^(2)+n_2^(2)+2n_1n_2costheta`
`=1+1+2costheta`
Since it is given that `n_S` is also a unit vector, therefore
`1=1+1+2costhetaimpliescostheta=-(1)/(2)becausetheta=120^@`
Now the difference vector is
`hatn+d=hatn_1-hatn_2 or n_d^(2)=n_1^(2)+n_2^(2)-2n_1n_2costheta=1+1-2costheta=1+1-2cos(120^@)`
`n_d^(2)=2-2((-1)/(2))=2+1=3impliesn_d=sqrt(3)`
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