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Final Exam Practice
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Exam of 11 pages for the course MATH 32A at MATH 32A (Final Exam Practice)
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Math 32A - Fall 2018Practice Final Exam
Full Name:
UID:
Circle the name of your TA and the day of your discussion:
Kevin Carlson Weiyi Liu Sang Truong
Tuesday Thursday
Instructions:
• Read each problem carefully.
• Show all work clearly and circle or box your final answer where
appropriate.
• Justify your answers. A correct final answer without valid reasoning
will not receive credit.
• Simplify your answers as much as possible.
• Include units with your answer where applicable.
• Calculators are not allowed but you may have a 3 × 5 inch notecard.
Page Points Score Page Points Score
1 10 7 12
2 10 8 10
3 8 9 6
4 10 10 10
5 12 Bonus
6 12 Total: 100
, 1. (2 points) Suppose u is a unit vector and v is a vector with ||v|| = 5. If the angle θ
between u and v has sin θ = 53 , find the length of u × v.
dB
2. (3 points) Given a curve with binormal B, show that is perpendicular to B.
ds
3. (5 points) Consider the planes 3x − 2y + z = 1 and 2x + y − 3z = 3, which intersect in
a line L.
(a) Notice that the point P = (1, 1, 0) is in the intersection of the planes and so is on
L. Use P to find a vector equation for L.
(b) If θ is the angle between the planes, find cos θ.
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