Question:

If vectors A = cos(ωt)i + sin(ωt)j and B = cos(ωt/2)i + sin(ωt/2)j are functions of times, then the value of t at which they are orthogonal to each other is:

t=0

t=π/2ω

t=π/4ω

t=πω

A and B are orthogonal to each other ⇒ A.B = 0
∴ cos(ωt)cos(ωt/2) + sin(ωt)sin(ωt/2) = cos(ωt - ωt/2) = cos(ωt/2) = 0
⇒ ωt/2 = π/2
⇒ t = π/ω