Question

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

Answer 1

Correct Answer - D
`vec(A)= cos omega t hat(i)+sin omega t hat(j)`
For `vec(A)` and `vec(B)` orthogonal `vec(A)vec(B)=0`
`(cos omega t hat(i)+sin omega t hat(j)).((cos)(omegat)/(2)hat(i)+(sin)(omegat)/(2)hat(j))=0`
`cos omega t.(cos)(omegat)/(2)+sin omega t.(sin)(omegat)/2=0`
`cos(omegat-(omegat)/(2))=0`
`implies (cos)(omegat)/(2)=0`
`(omegat)/(2)=(pi)/(2) implies omegat=pi implies t=(pi)/(omega)`