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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

`npi-(pi)/(6),n inZ`

B

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

C

`n pi+-(pi)/(6),n in Z`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
`sqrt(3) tan theta+1 =0 and sqrt(3) sec theta-2=0`
`implies theta=(11pi)/(6)`
`implies theta=2n pi+(11pi)/(6), n in Z`.
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