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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.vec0," "vecc.veca=vecc.vecb=cos theta`
`vecc.veca=lambda(veca.veca+veca.vecb)+mu veca. (veca xx vecb)`
`cos theta=lambda`
`vecc.vec=lambda^(2)(veca+vecb)^(2)+mu^(2)(1.1.sin90^(@))^(2)+2lambdamu((veca+vecb).(vecaxx vecb))`
`1=lambda^(2)(1+1+2.0)+mu^(2)+2lambdamu(0)`
`1=2cos^(2)theta+mu(2)+2lambdamu(0)`
`1=2cos^(2)theta+mu^(2)," "mu^(2)=1-2cos^(2)theta ge0`
`-(1)/(sqrt2) le cos theta le (1)/(sqrt2)," "theta in [(pi)/(4),(3pi)/(4)]`
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