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Unformatted text preview: yellow MULTIPLE CHOICE QUESTIONS ENTER ALL ANSWERS ON YOUR SCANTRON FORM 882ES (in pencil) If you change any answers on the scantron form, please make sure to erase completely and leave no smudges. 1 2 PROBLEM 1 (10 Points) The angle between two nonparallel planes is, by definition, the angle between their normal vectors. Calculate the angle between the planes 3 x + 2 y z = 2 , x + 3 y + 2 z = 5 (A) 0 (B) 3 (C) 4 (D) 6 (E) 2 PROBLEM 2 (10 Points) Compute the volume V of the parallelepiped spanned by the vectors u = ( 2 , 1 , ) , v = ( , , 3 ) , w = ( , 1 , 1 ) , (A) 0 (B) 3 (C) 4 (D) 6 (E) 9 3 PROBLEM 3 (10 Points) Compute the directional derivative of f ( x,y,z ) = xyz 2 at P = (3 , 2 , 1) in the direction of the vector i + k . (A) 157 (B) 14 2 (C) 14 (D) 14 2 (E) 157 2 PROBLEM 4 (10 Points) If the gradient vector of f ( x,y,z ) at a point P is f P = ( 2 , 3 , 3 ) , then the maximum value among the directional derivatives D e f ( P ) is (A) 0 (B) 16 (C) 4 (D) 9 (E) 13 4...
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This note was uploaded on 08/19/2009 for the course MATH 32A taught by Professor Gangliu during the Spring '08 term at UCLA.
 Spring '08
 GANGliu
 Multivariable Calculus

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