Exam 1 Review

# Exam 1 Review - Exam 1 will be given on Thursday Sept 30th...

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Exam 1 will be given on Thursday, Sept 30th, covering sections 12.1–12.5, 13.1-13.4. No make- up exam will be given unless you have an absolutely valid excuse. In the exam, show all your work and explain what you are doing. Answers will be graded on the accuracy and clarity of the work shown. 1. Review the relevant homework assignments. 2. Review all examples given in my lectures. 3. Let ~a = (6 , 2 , 3), ~ b = ( - 1 , 5 , 2) and ~ c = (1 , 0 , 1). Find (1) ~a + 3 ~ b - 2 ~ c ; (2) ~a · ~ b ; (3) ~a × ~ b ; (4) | ~ c | ; (5) Proj ~ c ~ b ; (6) the area of the parallelogram determined by ~a and ~ b . (7) the volume of the parallelepiped determined by ~a , ~ b and ~ c . 4. Find a parametric equation for the line through the points (3 , 1 , - 1) and (3 , 2 , - 6). 5. Find an equation for the plane through the points (3 , 1 , - 1), (3 , 2 , - 6) and (1 , 1 , 0). 6. Find an equation for the plane that passes the point (1 , 1 , - 1) and perpendicular to the line x = 2 t + 1 , y = 3 t - 2 , z = - 4 t + 1. 7. Find an equation for the plane consisting all points that are equidistant from the points (3 , 1 , - 1) and (3 , 2 , - 6). 8. Find parametric equations for the line of intersection of the planes 2 x + 5 z + 3 = 0 and x - 3 y + z + 2 = 0. 9. Find the distance between the point (3
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