HW08-solutions-1

# HW08-solutions-1 - zakaria (mmz255) – HW08 – gilbert...

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Unformatted text preview: zakaria (mmz255) – HW08 – gilbert – (55485) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Suppose you start at the origin in 3-space, move along the x-axis a distance of 7 units in the positive direction, and then move down- ward a distance of 6 units. What are the coordinates of your position? 1. (0 , − 6 , 7) 2. (7 , − 6 , 0) 3. (7 , , − 6) correct 4. (0 , 7 , − 6) 5. (7 , , 6) Explanation: We start at the origin, which has coordi- nates (0 , , 0). First we move 7 units along the positive x-axis, affecting only the x- coordinate, bringing us to the point (7 , , 0). We then move 6 units downward, in the nega- tive z-direction. Thus only the z-coordinate is affected, and so we arrive at the point having coordinates (7 , , − 6) . keywords: 3-space, coordinates, 002 10.0 points Which one of the points P ( − 3 , , − 8) , Q (0 , 5 , 0) , R (4 , − 3 , 1) in 3-space is closest to the xz-plane? 1. P ( − 3 , , − 8) correct 2. Q (0 , 5 , 0) 3. R (4 , − 3 , 1) Explanation: The distance of a point ( a, b, c ) in 3-space from the xz-plane is given by | b | . Conse- quently, of the three points P ( − 3 , , − 8) , Q (0 , 5 , 0) , R (4 , − 3 , 1) the one closest to the xz-plane is P ( − 3 , , − 8) . keywords: plane, distance in 3-space, 003 10.0 points A rectangular box is constructed in 3-space with one corner at the origin and other ver- tices at (5 , , 0) , (0 , 6 , 0) , (0 , , 3) . Find the length of the diagonal of the box. 1. length = 97 2. length = √ 97 3. length = 70 4. length = √ 70 correct 5. length = 9 6. length = 81 Explanation: We have to find the length of BD in the figure O D A B G F C E zakaria (mmz255) – HW08 – gilbert – (55485) 2 given that OA = 5 , OC = 6 , OD = 3 . Now by Pythagoras’ theorem, length OB = length AC = √ 61 . But then, again by Pythagoras, length BD = √ 70 . Consequently, length = √ 70 . keywords: length diagonal, rectangular solid, Pythagoras’ theorem, ThreeDimSys, 004 10.0 points Determine the distance of the point Q ( − 2 , 3 , 4) from the yz-coordinate plane. 1. distance = √ 29 2. distance = 2 √ 5 3. distance = 2 correct 4. distance = 4 5. distance = 3 6. distance = √ 13 7. distance = 5 Explanation: Since the distance of a point P ( x, y, z ) from the xy-, yz-, and zx-coordinate planes is given respectively by | z | , | x | and | y | , the point Q ( − 2 , 3 , 4) has distance = 2 from the yz-plane. keywords: coordinate plane, projection, point, distance, 3-space 005 10.0 points Determine the distance of the point Q (4 , 2 , − 3) from the z-axis. 1. distance = 5 2. distance = √ 29 3. distance = 3 4. distance = 2 5. distance = 4 6. distance = √ 13 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 radicalbig x 2 + y 2 , radicalbig y 2 + z 2 , radicalbig...
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## This note was uploaded on 06/05/2011 for the course MATH 408 D taught by Professor Gilbert during the Spring '11 term at University of Texas.

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HW08-solutions-1 - zakaria (mmz255) – HW08 – gilbert...

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