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Unformatted text preview: Math 20C Prof. Rabin First Midterm Exam, Version B October 22, 2007 Write your name and your section number or time at the top of this exam. You may not use notes, a calculator, or any other assistance. If any question is not clear, ask the instructor for clarification. Show all work necessary to justify your answers. Please box your answers and cross out any false starts. Each problem is worth 25 points. Good luck! (1) (a) Find the coordinates of the point where the line x = 3 t- 3 , y =- t + 2 , z = t- 3 intersects the plane x + y- 3 z = 6. Answer: Substitute the equations of the line into the equation of the plane as follows: x + y- 3 z = 6 (3 t- 3) + (- t + 2)- 3( t- 3) = 6- t + 8 = 6 t = 2 . Use t = 2 to find the point on the line, x = 3(2)- 3 = 3 y =- (2) + 2 = 0 z = (2)- 3 =- 1 so the point is (3 , , 1) . (b) Find the angle between the line and the normal vector to the plane....
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- Fall '08