# Final Spring 2014 - Northwestern University Math 230 Final...

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Northwestern University Math 230 Final 2014-06-10 Last name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Email . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NetID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instructions: This exam has 1 3 problems. Read each problem carefully. Write legibly. Cross off anything you do not wish graded. Write in complete sentences. Please make sure that all pages are included. You may not use books or notes. You have 120 minutes to complete this exam. Do not write near the edges of the page. Good luck!
Problem 1 (10 points) Find an equation for the plane containing the three points P ( 1, 2, 0 ) , Q ( - 1, 3, 1 ) and R ( 0, 1, 4 ) .
Problem 2 (20 points) Let P be the plane given by the equation x + y - 2 z = 3 (a) (8 points) Find parametric equations for the line L through ( 4, - 1, 3 ) that is perpendicular to the plane P . (b) (6 points) Find the point of intersection of the line L with the plane P . (c) (6 points) Find the distance from the point ( 4, - 1, 3 ) to the plane P .
Problem 3 (12 points) Two balloons are flying in the sky. Their paths (for t 0) are given by r 1 ( t ) = h t , 3 t , 12 t 2 + 3 t 3 i r 2 ( t ) = h 1, t , t 2 + 2 t i (a) (8 points) Do the paths of the balloons intersect? If so, where?