exam1Solutions

exam1Solutions - Name: Math 211A Fall 2005 Exam # 1 Honor...

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Name: Math 211A Fall 2005 Exam # 1 Honor Code Write and sign the honor code here after you have finished the quiz. There will be no calculators allowed during the exam. You may use a 3x5 inch note card. Use full sentences on all explanations and put a box around your final answer. Good Luck!! 1. True or False (2 points each) a. False The intersection of two surfaces is always a line. b. False The area of a parallelogram with sides ~a and ~ b is given by | ~a · ~ b | . c. True For any vectors ~a and ~ b , we have ~a · ( ~a × ~ b ) = 0. d. False The graph of f ( x, y ) = x + y sin x is a space curve. e. True Suppose r ( s ) defines a vector function which is parametrized by arclength. Then Z 1 0 | r 0 ( s ) | ds = Z 2 1 | r 0 ( s ) | ds .
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2. (a) (5 points) Find an equation of the line through the point (7 , 2 , - 5), which is parallel to the line x - 2 3 = y + 4 2 ; z = 3 . The line we are given has a direction vector of < 3 , 2 , 0 > . Therefore the line we are looking for goes through the point (7
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exam1Solutions - Name: Math 211A Fall 2005 Exam # 1 Honor...

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