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Unit vector vecc is inclined at an ang...

Unit vector `vecc` is inclined at an angle `theta` to unit vectors `veca and vecb` which are perpendicular.
If `vecc=lambda(veca+vecb)+mu(veca xx vecb), lambda, mu` real, then `theta` belongs to:

A

`(-(pi)/(4),0)`

B

`[0,(pi)/(4))`

C

`[(3pi)/(4),pi)`

D

`[(pi)/(4),(3pi)/(4)]`

Text Solution

Verified by Experts

The correct Answer is:
D
`veca.vecb=0 " " , vecc.veca= vecc.vecb=cos theta`
`vecc.veca= lambda(veca.veca.+veca.vecb)+muvec.(vecaxxvecb)`
`cos theta=lambda`
`vecc.vecc=lambda^(2)(veca+vecb)^(2)=mu^(2)(1*1 sin90^(@))+2lambdamu{(veca+vecb)*(vecaxxvecb)}`
`1=lambda^(2))1+1+2*0)+mu^(2)+2lambda (0)`
`1=cos^(2) theta+mu^(2), " " mu^(2)=1-2 cos^(2) theta ge0`
`-(1)/(sqrt(2)) le cos theta le(1)/(sqrt(2)), " " theta in [(pi)/(4),(3pi)/(4)]`
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