# Math22 - Math 22 Exam 1C Akers FS 00 \$ j\$ 1(15 pts Given a = 2i 3 \$ k and b = 1,0,4 and c = 1,1,1 find the following a b c d e A vector

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Math 22 Exam 1C Akers — FS 00 1) (15 pts) Given \$ \$ 23 ai jk =-+ \$ and 1,0,4 b =- 1,1,1 c = , find the following: a) A vector perpendicular to both a b . b) The scalar projection of b in the direction of a . c) A unit vector in the direction of b . d) The angle between a b . e) Prove a is orthogonal to c . 2.(8 pts) Given the vectors p q below, geometrically show pq + , 2 - , and × . 3.(10 pts) Find the equation of the plane that contains both the point (-1, 2, 1) and the line defined parametrically by 1 xt , yt = , and 3 zt . 4. (9 pts) Match the names of the following surfaces and the axis of orientation (axis of symmetry), and then choose one of the surfaces and sketch it. Label the graph with the chosen equation. Surface Name Axis 22 30 x yz -+= _______ ____ a. ellipsoid b. cone c. parabolic cylinder 2 3 += _______ ____ d. hyperbolic paraboloid e. elliptic paraboloid f. hyperboloid of 1 sheet 222 3 10 xyz -+ += _______ ____ g. hyperboloid of 2 sheets 5a. (7 pts) Find the distance from the point (1,1,-2) to the plane 28 x yz . 5b. (8 pts) Find the point (x,y,z) on the plane in problem #5 that is closest to the point (1,1,-2). HINT: Consider the line L that contains the point

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## This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.

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Math22 - Math 22 Exam 1C Akers FS 00 \$ j\$ 1(15 pts Given a = 2i 3 \$ k and b = 1,0,4 and c = 1,1,1 find the following a b c d e A vector

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