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Part Two Exercises involving 3 dimensional curves

5.(a) describe the curve defined by


(b) describe the curve defined by


6.(a) consider the curves defined by


what roles do a, b and c play in the shape of the curves? >

(b) from part a, set a and b to 1 and c to 2. How much vertical increase in z is there for each revolution around the z axis? This quantity is called ``pitch".

7. Describe the curves in tex2html_wrap_inline186 defined by


in particular, what effect do A, B and w have on the curve? Take as a starting point values A=10, B=1, and w=16; also numpoints=500 helps.

8. The French racing team is driving their race car around a track, with their position described by tex2html_wrap_inline196 They are practicing for an upcoming race. Meanwhile, the Hungarian endurance racing team is driving cross country to test their equipment and endurance for another upcoming race. Their position at any time tex2html_wrap_inline198 is described by (60t - 20, -30t +11) .

(a) Will the Hungarian team ever cross the race track? If so, where?

(b) Will the Hungarian and French cars collide? If so, where?

(c) How long is the race track?

Note: all expressions above are in miles and hours. If any integrals are needed, evalf(int may produce better results than int.

J. Goulet
Wed Feb 19 11:13:36 EST 1997