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The resultant of two vectors vecA and ve...

The resultant of two vectors `vecA` and `vecB` is perpendicular to the vector `vecA` and its magnitude is equal to half of the magnitude of the vector `vecB`. Find out the angles between `vecA` and `vecB`.
.

A

`120^@`

B

`150^@`

C

`135^@`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(B)/(2)=sqrt(A^(2)+B^(2)+2ABcostheta)`
`tan90^@=(Bsintheta)/(A+Bcostheta)impliesA+Bcostheta=0`
`costheta=-(A)/(B)`
Hence, from (i) `(B^(2))/(4)=A^(2)+B^(2)-2A^(2)impliesA=sqrt(3)(B)/(2)`
`impliescostheta=-(A)/(B)=-(sqrt(3))/(2)becausetheta=150^@`
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