Math 192 Prelim 1, Feb. 21, 2006 Calculators are not allowed. Write your section number and TA’s name on the front of your workbook. This exam is worth 100 points. Point values for each problem are in parentheses. 1. Let ~u =-2 ~ i + 4 ~ j-~ k and ~v = 2 ~ i + 3 ~ j-6 ~ k be two vectors in 3-space. a) (5) Find the angle between ~u and ~v. b) (4) Find a vector ~w of magnitude 5 units in the direction opposite to that of ~u + ~v. c) (4) Let ~u , ~v , and ~w be arbitrary vectors. Answer as True or False. (No reasons needed.) i) If ~u x ~v = ~u x ~w and ~u 6 = ~ 0, then ~v = ~w. ii) If ~u 6 = ~0 ,~u x ~v = ~u x ~w and ~u · ~v = ~u · ~w , then ~v = ~w. 2. a) (8) Find the line of intersection of the planes 2 x-y + 3 z = 4 and-x + y + 2 z = 1. Then ﬁnd the plane perpendicular to this line and containing the point (5 , 6 ,-3) . b) (6) Find the distance between the two planes 2 x + 3 y-z = 4 and 2 x + 3 y-z = 9 . 3. Let
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This note was uploaded on 02/28/2008 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).