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Assignment 3

# Assignment 3 - patino(mp25752 Assignment3 luecke(57510 This...

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patino (mp25752) – Assignment3 – luecke – (57510) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Which one of the points P (1 , 6 , 4) , Q (9 , 8 , 7) , R ( 5 , 5 , 8) in 3-space is closest to the yz -plane? 1. P (1 , 6 , 4) correct 2. Q (9 , 8 , 7) 3. R ( 5 , 5 , 8) 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 , 6 , 4) , Q (9 , 8 , 7) , R ( 5 , 5 , 8) the one closest to the yz -plane is P (1 , 6 , 4) . keywords: plane, distance in 3-space, 002 10.0 points Which of the following statements are true: A. in 3 -space the pair of equations braceleftbigg x = 5 , z = 4 , represents a line , B. in 2 -space the equation x = 5 represents a line . 1. both of them correct 2. B only 3. neither of them 4. A only Explanation: A. TRUE: in 3 -space the equation x = 5 represents a planeperpendicular tothe x -axis, while z = 4 represents a plane perpendicular to the z -axis. But together the equations represent the intersection of these two planes, i.e. , a line . B. TRUE: in the plane the graph of x = 5 is a vertical line . keywords: T/F, True/False, plane, 2-space, 3-space, point 003 10.0 points A triangle Δ PQR has vertices P (2 , 1 , 1) , Q (1 , 0 , 2) , R (3 , 2 , 2) . Use the distance formula to decide which one of the following properties the triangle has. 1. isoceles with | QP | = | QR | 2. not isoceles 3. isoceles with | RP | = | RQ | 4. isoceles with | PQ | = | PR | correct Explanation: Recall that for points A, B it is common to denote the line segment from A to B by AB ,

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Assignment 3 - patino(mp25752 Assignment3 luecke(57510 This...

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