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Unformatted text preview: HKUST MATH 101 Midterm Examination Multivariable Calculus 14 October 2004 Answer ALL 5 questions Time allowed – 120 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 Total /100 Problem 1 (a) If e is any unit vector and a an arbitrary vector show that a = ( a · e ) e + e × ( a × e ) . This shows that a can be resolved into a component parallel to and one perpendicular to an arbitrary direction e . (b) Show that the two lines r = a + v t, r = b + u t where t is a parameter and u and v are two unit vectors, will intersect if a · ( u × v ) = b · ( u × v ) ....
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- Spring '11
- Multivariable Calculus