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

Options

A. t=0
B. `t=(pi)/(4omega)`
C. `t=(pi)/(2omega)`
D. `t=(pi)/(omega)`

Answer

D

Explanation

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)`