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If a and b are the two vectors such that...

If a and b are the two vectors such that `|a|-3sqrt(3),|b|=4` and `|a+b|=sqrt(7)`, then the angle between a and b is

A

`120^(@)`

B

`60^(@)`

C

`30^(@)`

D

`150^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
Since
`|a+b|^(2)=|a|^(2)+|b|^(2)+2|a||b|cos theta`
`implies(sqrt(7))^(2)=(3sqrt(3))^(2)+4^(2)`
`+2(3sqrt(3))(4)cos theta`
`implies7=27+16+24sqrt(3)cos theta`
`impliescos theta =(sqrt(3))/2`
`implies theta=150^(@)`
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