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If the vectors `vec a` and `vec b`are linearly independent and satisfying `(sqrt3tantheta+1)vec a + (sqrt3sectheta-2)vec b=vec 0`,then the most general values of `theta` are:

A

`2npi - (pi)/(6), n in Z`

B

`2n pi pm (11pi)/(6), n in Z`

C

`n pi pm (pi)/(6), n in Z`

D

`2 npi + (11pi)/(6), n in Z`

Text Solution

Verified by Experts

The correct Answer is:
D
`sqrt3 tan theta +1 =0 and sqrt3 sectheta -2=0`
`rArr theta = (11 pi)/(6)`
`rArr " " theta = 2npi + (11pi)/( 6), n in Z`
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