midterm 2005

midterm 2005 - HKUST MATH 102 Midterm Examination Problem...

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HKUST MATH 102 Midterm Examination Multivariable and Vector Calculus 21 Dec 2005 Answer ALL 8 questions Time allowed – 180 minutes Directions – This is a closed book examination. No talking or whispering are allowed. Work must be shown to receive points. An answer alone is not enough. Please write neatly. Answers which are illegible for the grader cannot be given credit. Note that you can work on both sides of the paper and do not detach pages from this exam packet or unstaple the packet. Student Name: Student Number: Tutorial Session: Question No. Marks 1 /20 2 /20 3 /20 4 /20 5 /20 6 /20 7 /20 8 /20 Total /160 Problem 1 (a) Assume a , b and c are three dimensional vectors and if ( a × b ) × c = λ a + μ b + β c . Use suFx notation to ±nd λ , μ and β in terms of the vectors a , b and c . Can you say something about the direction of the vector ( a × b ) × c . (b) Let a be a constant vector and r = ( x, y, z ), use suFx notation to evaluate (i) ∇ · r , (ii) ∇ · ( a
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midterm 2005 - HKUST MATH 102 Midterm Examination Problem...

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