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Two time-dependent vectors are given by A = cos(ω t) î + sin(ω t) ĵ and B = cos ((ω t)/(2)) î + sin ((ω t)/(2)) ĵ. At what value of t are these vectors perpendicular to each other?

1. t = (π)/(2ω)
2. t = (π)/(ω)
3. t = 0
4. t = (π)/(4ω)

Correct answer: t = (π)/(ω)

Solution

A.B = cos(wt)cos(wt/2) + sin(wt)sin(wt/2) = cos(wt - wt/2) = cos(wt/2). Setting this to zero gives wt/2 = pi/2, hence t = pi/w.

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