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If Vectors vec(A)= cos omega t(i)+ sin o...

If Vectors `vec(A)= cos omega t(i)+ sin omega t(j)` and `vec(B)=cosomegat/(2)hat(i)+sinomegat/(2)hat(j)`are functions of time. Then the value of `t` at which they are orthogonal to each other is

A

t=0

B

`t=(pi)/(4omega)`

C

`t=(pi)/(2omega)`

D

`t=(pi)/(omega)`

Text Solution

Verified by Experts

The correct Answer is:
D
For perpendicular
`vecA.vecB=0`
`implies[cosomegathati+sinomegathatj]*["cos"(omegat)/(2)hati+"sin"(omegat)/(2)hatj]=0`
`cosomegat"cos"(omegat)/(2)+sinomegat"sin"(omegat)/(2)=0`
`{because cosA cosB+sinAsinB=cos(A-B)}`
`thereforecos(omegat-(omegat)/(2))=0`
`implies"cos"(omega)/(2)=0`
`implies(omegat)/(2)=(pi)/(2)`
`impliest=(pi)/(omega)`
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