This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: zakaria (mmz255) – HW08 – gilbert – (55485) 1 This printout should have 23 questions. Multiplechoice 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 3space, move along the xaxis 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 xaxis, affecting only the x coordinate, bringing us to the point (7 , , 0). We then move 6 units downward, in the nega tive zdirection. Thus only the zcoordinate is affected, and so we arrive at the point having coordinates (7 , , − 6) . keywords: 3space, coordinates, 002 10.0 points Which one of the points P ( − 3 , , − 8) , Q (0 , 5 , 0) , R (4 , − 3 , 1) in 3space is closest to the xzplane? 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 3space from the xzplane 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 xzplane is P ( − 3 , , − 8) . keywords: plane, distance in 3space, 003 10.0 points A rectangular box is constructed in 3space 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 yzcoordinate 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 zxcoordinate planes is given respectively by  z  ,  x  and  y  , the point Q ( − 2 , 3 , 4) has distance = 2 from the yzplane. keywords: coordinate plane, projection, point, distance, 3space 005 10.0 points Determine the distance of the point Q (4 , 2 , − 3) from the zaxis. 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 yaxes is given respec tively by radicalbig x 2 + y 2 , radicalbig y 2 + z 2 , radicalbig...
View
Full
Document
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.
 Spring '11
 Gilbert

Click to edit the document details