- #1
negation
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Homework Statement
Show that if the vector function r(t) is continuously differentiable for t on an interval I and |r(t)| = c, a constant for all t [itex]\in I[/itex], then r'(t) is orthorgonal to r(t) for all t [itex]\in I[/itex]
What would the curve described by r(t) look like?
The Attempt at a Solution
The solution is given as:
|r(t)|2 = r(t) . r(t)
r(t).r(t) = c2 ( I can see the algebraic reasoning for this but what's the conceptual reasoning behind?)
then,
r'(t).r(t) + r(t).r'(t) = 0
that is, 2r'(t) .r(t) = 0. Hence r'(t) is orthorgonal to r(t) for all t.
What is the question I should be asking myself?