HW08-solutions - moore (jwm2685) – HW08 – gilbert –...

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Unformatted text preview: moore (jwm2685) – 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 3 units in the positive direction, and then move down- ward a distance of 2 units. What are the coordinates of your position? 1. (0 , 3 , − 2) 2. (3 , , − 2) correct 3. (3 , , 2) 4. (3 , − 2 , 0) 5. (0 , − 2 , 3) Explanation: We start at the origin, which has coordi- nates (0 , , 0). First we move 3 units along the positive x-axis, affecting only the x- coordinate, bringing us to the point (3 , , 0). We then move 2 units downward, in the nega- tive z-direction. Thus only the z-coordinate is affected, and so we arrive at the point having coordinates (3 , , − 2) . keywords: 3-space, coordinates, 002 10.0 points Which one of the points P ( − 1 , 9 , 8) , Q (3 , 1 , 0) , R (5 , , 9) in 3-space is closest to the yz-plane? 1. P ( − 1 , 9 , 8) correct 2. Q (3 , 1 , 0) 3. R (5 , , 9) Explanation: The distance of a point ( a, b, c ) in 3-space from the yz-plane is given by | a | . Conse- quently, of the three points P ( − 1 , 9 , 8) , Q (3 , 1 , 0) , R (5 , , 9) the one closest to the yz-plane is P ( − 1 , 9 , 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 (4 , , 0) , (0 , 3 , 0) , (0 , , 5) . Find the length of the diagonal of the box. 1. length = √ 43 2. length = √ 34 3. length = 34 4. length = 5 √ 2 correct 5. length = 50 6. length = 43 Explanation: We have to find the length of BD in the figure O D A B G F C E moore (jwm2685) – HW08 – gilbert – (55485) 2 given that OA = 4 , OC = 3 , OD = 5 . Now by Pythagoras’ theorem, length OB = length AC = 5 . But then, again by Pythagoras, length BD = 5 √ 2 . Consequently, length = 5 √ 2 . keywords: length diagonal, rectangular solid, Pythagoras’ theorem, ThreeDimSys, 004 10.0 points Determine the distance of the point Q (5 , − 2 , 1) from the yz-coordinate plane. 1. distance = 1 2. distance = 2 3. distance = √ 30 4. distance = 5 correct 5. distance = √ 5 6. distance = √ 29 7. distance = √ 26 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 (5 , − 2 , 1) has distance = 5 from the yz-plane. keywords: coordinate plane, projection, point, distance, 3-space 005 10.0 points Determine the distance of the point Q (5 , 3 , − 2) from the y-axis. 1. distance = 2 2. distance = 5 3. distance = 3 4. distance = √ 13 5. distance = √ 38 6. distance = √ 29 correct 7. distance = √ 34 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 z 2 + x 2 , the point...
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This note was uploaded on 04/21/2011 for the course M 408 D taught by Professor Textbookanswers during the Spring '07 term at University of Texas.

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HW08-solutions - moore (jwm2685) – HW08 – gilbert –...

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