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calc 3 test 1 - ”7 CI” r m ’H mm W it(ill m it J X...

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Unformatted text preview: ”7 CI”) ., r - m ’H) , mm W; it (ill . , m it J * X ‘/ North Carolina State University MA 242 Section 007 Exam 1 Read all directions carefully. A graphing calculator may NOT be used on this exam. You must Show All Work for credit and clearly indicate your final answer; no work equals no credit. When you are finished fold your exam, write your name on the outside, turn it in, and then you may leave quietly. Good Luck! True/ False section a) (3 pts) The curvature of a line is zero. b) (3 pts) FOE) =< t2, ln(t2) > is a parametrization of the function y = ln(x). c) (3 pts) 17 X (‘55 73) is a scalar. Computations ‘~ 1) (15 pts) Compute the dot product of the vectors €>=< 1, O, o > and {i =< —1§ ~—%, 21; >. Are these vectors orthogonal? 2) (20 pts) Find the equation of the plane that contains the two parallel lines m) :< 1+t,~2— 2t,3t > and fit) =< 2+t,3— 225,1 +3t >. 3) (15 pts)HW#16 Find the velocity vector of a particle that has acceleration 6(1‘) = ti + c‘j + 5% and initial velocity 170 z: k. 4) (20 pts) Calculate the curvature K7 of the curve F(t) =< cos(t), 4, sin(t) >. 5) (10 pts) Given 121, u}, and a]; are orthogonal unit vectors, (1' = (1,1131 + (12%} + ago}, and b 2 (no? + 13312}, compute if - b 6) HW #34 If 6;, v3, and 175, are non coplaner vectors and we define the vector a) (5 pts) Show that I; is orthogonal to 172. b) (5 pts) Show that k: 451 = l. BONUS (+5 pts) Show that the acceleration vector of a curve is orthogonal to the velocity vector if the » speed is constant. ...
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