Unformatted text preview: where x = y . 4. Let c ( t ) be a path in R 3 that does not pass through the origin. If c ( t ) is a point on the path that is closest to the origin, show that the position vector c ( t ) is orthogonal to the velocity vector c ′ ( t ). 5. ±ind the length of the curve c ( t ) = ( t, (2 / 3) t 3 / 2 ), 0 ≤ t ≤ 8. 6. ±ind the point on the curve c ( t ) = (5 sin t, 5 cos t, 12 t ) that is a distance of 26 π units along the curve from the point c (0). 7. The path c ( t ) = ( a cos 3 t, a sin 3 t ) traces out a curve known as an astroid. Sketch this curve and compute its total length. (This is exercise 7 in section 3.2.)...
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 Spring '08
 PARKINSON
 Math, Multivariable Calculus

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