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Exam 1 Choike Fall 2010

# Exam 1 Choike Fall 2010 - • MATH 2163 Calculus III Exam 1...

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Unformatted text preview: • MATH 2163, Calculus III Exam 1 I. (10 pts.) Place yourself at the point (-2,4, -3) in the xyz-coordinate system. a. Starting at this point, move 5 units in the direction of the yz-plane; stop and make a right turn of 90° and move in this new direction another 8 units; stop and finally lower yourself 2 units. What are the coordinates of this new location? ('3-'1)~ b. What is the distance from your original position to your final position? ' 1IPf 2. (20 pts) Given the two vectors v =-31 + 2] - k and w = 1- 2] + 3k . a. What is the vector 3v - 2w? b. Find the dot product v. (3v - 2w). c. Find the angle between the vectors v and w . vH):: (U-6); f(U-t)J to{z-/tJt+ ..,)'h a. Find the velocity vector vet) and the acceleration vector a(t). cd.f) = 21:. +- Zj +(f>t -IO)"t d. Find the vector projection of the vector v onto the vector w. . L:-17 /% )_JX > 3. (15 pts) Find the equation of the plane passing through the point (-~, -2,3) and perpendicular to both the planes x - 3y + 2z =7 and 2x - 2y - z...
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Exam 1 Choike Fall 2010 - • MATH 2163 Calculus III Exam 1...

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