# Prove that if a vector valued function r(t) has a constant length then r(t) and r0(t) are orthogonal.?

Update:

correction: Prove that if a vector valued function r(t) has a constant length then r(t) and r'(t) are orthogonal.?

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- RockItLv 75 years agoFavorite Answer
|r(t)| = constant implies that

1. r(t) either doesn't change with t, r'(t)=0 or

2. its direction is changing while its length remains constant. If r(t) only changes direction with t, then r'(t) is perpendicular to r(t). If this were not true, then r(t)'s length would change also by the triangle inequality. In either case since 1. r'(t)=0 or 2. r(t) dot r'(t) = r(t)r'(t)cos(90) = 0

Therefore, r(t) and r'(t) are orthogonal

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