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The maximum value of |(1,1,1),(1,1+sinth...

The maximum value of `|(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|` is `1/2`

A

`1/2`

B

`(sqrt(3))/2`

C

`sqrt(2)`

D

`(2sqrt(3))/4`

Text Solution

Verified by Experts

The correct Answer is:
A
Since
`Delta=|(1,1,1),(1,1+sintheta,1),(1+costheta,1,1)|`
`=|(0,0,1),(0,sintheta,1),(costheta,0,1)| [ :'C_(1)toC_(1)-C_(3)` and `C_(2)toC_(2)-C_(3)]`
`=1(sintheta.costheta)`
`=1/2.2sin theta cos theta=1/2sin 2theta`
Since the maximum value of `sin 2theta` is 1. So, for maximum valoue of `theta` should be `45^(@)`
`:. Delta=1/2sin 2.45^(@)`
`=1/2sin90^(@)=1/2.1=1/2`
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