Preliminary Questions

Question 13.1

Which one of the following does not parametrize a line?

  • r1(t) = 〈8 − t, 2t, 3t〉

  • r2(t) = t3i − 7t3j + t3k

  • r3(t) = 〈8 − 4t3, 2 + 5t2, 9t3〉

Question 13.2

What is the projection of r(t) = ti + t4j + et k onto the xz-plane?

Question 13.3

Which projection of 〈cos t, cos 2t, sin t〉 is a circle?

Question 13.4

What is the center of the circle with parametrization

r(t) = (−2 + cos t)i + 2j + (3 − sin t)k?

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Question 13.5

How do the paths r1(t) = 〈cos t, sin t〉 and r2(t) = 〈sin t, cos t〉 around the unit circle differ?

Question 13.6

Which three of the following vector-valued functions parametrize the same space curve?

  • (−2 + cos t)i + 9j + (3 − sin t)k

  • (2 + cos t)i − 9j + (−3 − sin t)k

  • (−2 + cos 3t)i + 9j + (3 − sin 3t)k

  • (−2 − cos t)i + 9j + (3 + sin t)k

  • (2 + cos t)i + 9j + (3 + sin t)k