hw3 - This print-out should have 15 questions....

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This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points A rectangular box is constructed in 3-space with one corner at the origin and other ver- tices at (4 , 0 , 0) , (0 , 3 , 0) , (0 , 0 , 1) . ±ind the length oF the diagonal oF the box. 1. length = 19 2. length = 26 correct 3. length = 34 4. length = 34 5. length = 26 6. length = 19 Explanation: We have to fnd the length oF BD in the fgure O D A B G F C E given that OA = 4 , OC = 3 , OD = 1 . Now by Pythagoras’ theorem, length OB = length AC = 5 . But then, again by Pythagoras, length BD = 26 . Consequently, length = 26 . keywords: length diagonal, rectangular solid, Pythagoras’ theorem 002 10.0 points Determine the distance oF the point Q ( 4 , 2 , 1) From the z -axis. 1. distance = 1 2. distance = 5 3. distance = 2 4. distance = 21 5. distance = 4 6. distance = 17 7. distance = 2 5 correct Explanation: Since the distance oF a point P ( x, y, z ) From the z -, x -, and y -axes is given respec- tively by r x 2 + y 2 , r y 2 + z 2 , r z 2 + x 2 , the point Q ( 4 , 2 , 1) has distance = 2 5 From the z -axis. keywords: coordinate plane, projection, point, distance, 3-space 003 10.0 points Which oF the Following statements are true:
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A. in 3 -space the pair of equations b x = 3 , z = 6 , represents a line , B. in 2 -space the pair of equations b x = 2 , y = 6 , represent a line . 1. neither of them 2. both of them 3. A only correct 4. B only Explanation: A. TRUE: in 3 -space the equation x = 3 represents a plane perpendicular to the x -axis, while z = 6 represents a plane perpendicular to the z -axis. But together the equations represent the intersection of these two planes, i.e. , a line . B. FALSE: in the plane the pair of equa- tions x = 2 and y = 6 represents a point . keywords: T/F, True/False, plane, 2-space,
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This note was uploaded on 09/28/2008 for the course M 408M taught by Professor Gilbert during the Fall '07 term at University of Texas.

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hw3 - This print-out should have 15 questions....

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