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Unit vectors veca and vecb ar perpendicu...

Unit vectors `veca and vecb` ar perpendicular , and unit vector `vecc` is inclined at an angle `theta` to both `veca and vecb . If alpha veca + beta vecb + gamma (veca xx vecb)` then.

A

`pi/4lethetalepi/4`

B

`pi/4lethetale(3pi)/4`

C

`0 le thetale pi/4`

D

`0 le thetale(3pi)/4`

Text Solution

Verified by Experts

The correct Answer is:
a
`vecc = mveca + nvecb + p(veca xx vecb)`
taking dot product with `veca and vecb` we have
`m =n= cos theta`
`Rightarrow |vecc|= |cos theta veca + cos theta veca + cos theta vecb + p (veca xx vecb)|=1`
squaring both sides, we get
`cos^(2)theta + cos ^(2) theta + p^(2) =1 `
`or cos theta= +-sqrt(1-p^(2))/sqrt2`
Now ` - 1/sqrt2 le cos theta ge 1/sqrt2` ( for real value of `theta`)
`pi/4 le cos theta le (3pi) / 4`
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