So there is this question I've been trying to work out, but couldn't come up with a positive answer. Any help on this is highly appreciated.

Question

Question : If n,a,b are constants and p is a vector : p=a cos nt + b sin nt.
Prove that p*dp/dt=na*b

So I worked out up to the below:
p*dp/dt=(a cos nt + b sin nt)n(b cos nt -a sin nt)

Answer 1

So there is this question I've been trying to work out, but couldn't come up with a positive answer. Any help on this is highly appreciated.

Question : If n,a,b are constants and p is a vector : p=a cos nt + b sin nt.
Prove that p*dp/dt=na*b

So I worked out up to the below:
p*dp/dt=(a cos nt + b sin nt)n(b cos nt -a sin nt)
=n{ [ab(cos^2(nt) - sin^2(nt))] - [ (b^2-a^2)sin nt*cos nt ] }

Answer 2

Maybe that's because it isn't true.
Let p = cost + sint
p' = cost - sint
p*p' = cos2t, not 1

Note that p = √(a^2+b^2) cos(nt-θ)
where cosθ = a/√(a^2+b^2)
clearly p*p' is not a constant