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.?

1 Answer

Relevance
  • RockIt
    Lv 7
    5 years ago
    Favorite 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

Still have questions? Get your answers by asking now.