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Let vecr = (veca xx vecb)sinx + (vecb xx...

Let `vecr = (veca xx vecb)sinx + (vecb xx vecc)cosy+(vecc xx veca)`, where `veca,vecb` and `vecc` are non-zero non-coplanar vectors, If `vecr` is orthogonal to `3veca + 5vecb+2vecc`, then the value of `sec^(2)y+"cosec"^(2)x+secy" cosec "x` is

A

3

B

4

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
A
`vecr. (3veca+5vecb+2vecc)=0`
`rArr veca.(vecb xx vecc)[2sin x+3 cosy+5]=0`
`rArr 2sinx+3cosy=-5` `(therefore veca.(vecb xx vecc) ne 0)`
`rArr sinx=-1, cosy=1`
`rArr "cosec "x=-1, secy=-1`.
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