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(MATH100)quiz01-1b.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: T1B

Answer ALL of the following 4 short answer questions. Show all your work for full credit.
1. (2 Marks) What is the cosine of the angle between the vectors .0, 6, .8. and .1, .1, .1..
Answer: cos equals:
2. (3 Marks) Write down the parametric equations of the line through Q = (0, 3, 4) which is perpen-
dicular to both lines
x . 1 y . 2 z . 2 x . 3 z . 1

L1 : == and L2 := ,y =3.
1 .1 .2 .11
Answer: The equations of line is:
3. (2 Marks) Let
r(t)= .3 cos t, 3 sin t, 2t. for . <t< .
What is the unit tangent vector to r(t) at t =?
6
Answer: The unit tangent vector is:
R3
4. (3 Marks) Let C be the curve in de.ned by the parametric equations
x(t) = cos(e t),y(t) = sin(e t),z(t)= e t fortin [0, 2]. What is the length of C ?
Answer: The length of C is: