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# Test1Old - MATH 231 Calculus III Section 1 Fall 2007 Test 1...

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MATH 231, Calculus III, Section 1, Fall 2007 Test 1 Date: Sep. 26, Wednesday Time: 10:00 am - 10:50 am Please write clearly, reduce answers to their simplest form, and box your answers. To receive full credit you must show ALL your work. Student's Name (Please print): __________________________________________ Pledge: On my honor as a student at the University of Virginia I have neither given nor received aid on this test. Signature: _______________________________ Problem Points Score 1 10 2 15 3 15 4 10 5 15 6 10 7 25 8 (Bonus) 10 Total 110/100

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Problem 1 (10 points) Let the vectors a and b be given by a = j - k and b = 2 i + j + 3 k . Find: (a) (2 points) the dot product of a and b (b) (4 points) the cross product of a and b (c) (4 points) the angle between the vectors a and b Problem 2 (15 points) The velocity of a particle is given by v ( t ) = cos 2 t i + sin t j . If the position of the object at time t = π 4 is at the point (2 , 0), find its position vector. 1
Problem 3 (15 points) (a) (8 points) Find parametric equations of the line L 1 through the point ( - 1 , 0 , 2) and parallel to the line L 2 given by the equations

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