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# yellowfinal.mc - yellow MULTIPLE CHOICE QUESTIONS ENTER ALL...

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Unformatted text preview: yellow MULTIPLE CHOICE QUESTIONS ENTER ALL ANSWERS ON YOUR SCANTRON FORM 882-ES (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 θ between two non-parallel planes is, by definition, the angle between their normal vectors. Calculate the angle θ between the planes 3 x + 2 y − z = 2 , x + 3 y + 2 z = 5 (A) 0 (B) π 3 (C) π 4 (D) π 6 (E) π 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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yellowfinal.mc - yellow MULTIPLE CHOICE QUESTIONS ENTER ALL...

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