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If three vectors (sec^(2)A) hati+hatj+ha...

If three vectors `(sec^(2)A) hati+hatj+hatk`, `hati+(sec^(2)B)hatj+hatk,hati+hatj+sec^(2)hatk` are complnar, then the value of `cosec^(2)A + cosec^(2)B+ cosec^(2)C` is -

A

1

B

2

C

3

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`|{:(sec^(2)A,1,1),(1,sec^(2)B,1),(1,1,sec^(2)C):}|`
`tan^(2)Atan^(2)Btan^(2)C+tan^(2)Atan^(2)B+tan^(2)Ctan^(2)B+tan^(2)Ctan^(2)A=0`
`cot^(2)A+cot^(2)B+cot^(2)C+1=0`
`"cosec"^(2)A+"cosec"^(2)B+"cosec"^(2)C=2`
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CAREER POINT-MOCK TEST 5-Part (C) (MATHS)
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