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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 xyzcoordinate system. a. Starting at this point, move 5 units in the direction of the yzplane; 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):: (U6); f(Ut)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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This note was uploaded on 01/10/2012 for the course MATH 2163 taught by Professor Staff during the Spring '08 term at Oklahoma State.
 Spring '08
 staff
 Calculus

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