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(MATH100)quiz01-1a.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: T1A
Answer ALL of the following 4 short answer questions. Show all your work for full credit.
1. (2 Marks) What is the magnitude of the projection of the vector .1, 2, 3. onto the vector .4, 3, 2. ?
Answer: The length of the projection is:
R3
2. (3 Marks) The equations of planes below de.ne a line of intersection L in , x + y =1,x + z =1.
Find an equation which de.nes a plane that is perpendicular to L and passes through the point (1, 1, 1).
Answer: The equation of plane is:
R3
3. (2 Marks) The position vector to a curve in is given by
.cos t, cos t, 2 sin t..

What is the unit tangent vector at t =?
3
Answer: The unit tangent vector is:
R3
4. (3 Marks) The coordinates of an object moving in at time t are
2
23
x = t, y = t, z = t.
3 What is the distance traveled by the object between t = 0 and t =3?
Answer: The distance is: