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(MATH100)quiz01-1c.pdf
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MATH 100 (L1) Introduction to Multivariable Calculus Spring 2006-07
. Quiz 01 (March 2, 2007): Vectors, Vector-valued Functions Duration: 40 minutes Name: ID No.: Tutorial Section: T1C
Answer ALL of the following 4 short answer questions. Show all your work for full credit.
1. (3 Marks) Find a vector n perpendicular to the plane P determined by the points A(1, .1, 0), B(2, 1, .1), and C(.1, 1, 2).
Answer: The vector n equals:
2. (2 Marks) Find the parametric equations of the line tangent to the graph of
r(t)= ti + t 2j
at the point (1, 1) on the curve.

Answer: The parametric equations are:
R3
3. (2 Marks) The coordinates of an object moving through are
1
x = at sin t, y = at cos t, z = bt2 ,
2
for time t> 0, where a, b, and c are constants. What is the speed of the object at any time t ?
Answer: The speed is:
R3
4. (3 Marks) Let C be the curve in de.ned by the parametric equations
x(t)=2t, y(t) = ln t, z(t)= t 2 fortin [1, 2]. What is the length of C ?
Answer: The length of C is: