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michonamona
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Homework Statement
Let u(t) be a vector valued function, where
u(t) = r(t).(r'(t)Xr''(t))
where r(t) is a vector valued function, and (r'(t)Xr''(t)) the cross product of the first and second derivative of r(t). Show that
u'(t) = r(t).(r'(t)Xr'''(t))
where r'''(t) is the 3rd derivative of r(t).
Homework Equations
The Attempt at a Solution
I got this question on an exam and did not know how to solve it. I started out by computing the cross product of (r'(t)Xr''(t)) by using determinants, and then took the dot product of r(t).(r'(t)Xr''(t)), which gave me a really ugly vector. I ran out of time while computing r(t).(r'(t)Xr'''(t)). Is there some other technique I could've applied to prove this?
Thanks,
M