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Unformatted text preview: patino (mp25752) – Assignment5 – luecke – (57510) 1 This printout should have 15 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Which of the following statements are true for all lines and planes in 3space? I. two lines perpendicular to a third line are parallel , II. two lines perpendicular to a plane are parallel , III. two planes parallel to a third plane are parallel . 1. I and III only 2. II only 3. I and II only 4. II and III only correct 5. III only 6. all of them 7. none of them 8. I only Explanation: I. FALSE: the xaxis and yaxis are perpen dicular, not parallel, yet both are perpendic ular to the zaxis. II. TRUE: the two lines will have direction vectors parallel to the normal vector of the plane, and so be parallel, hence the two lines are parallel. III. TRUE: each of the two planes has a normal vector parallel to the normal vector of the third plane, and so are parallel, hence the planes are parallel. 002 10.0 points Which of the following surfaces is the graph of 4 x + 3 y + 6 z = 12 in the first octant? 1. x y z 2. x y z 3. x y z 4. x y z patino (mp25752) – Assignment5 – luecke – (57510) 2 5. x y z 6. x y z cor rect Explanation: Since the equation is linear, it’s graph will be a plane. To determine which plane, we have only to compute the intercepts of 4 x + 3 y + 6 z = 12 . Now the xintercept occurs at y = z = 0, i.e. at x = 3; similarly, the yintercept is at y = 4, while the zintercept is at z = 2. By inspection, therefore, the graph is x y z 003 10.0 points Which equation has the surface x y z y z as its graph? 1. z − x = 1 2. y + z = 1 correct 3. x + z = 1 4. x + y = 1 5. y − x = 1 6. z − y = 1 Explanation: As the surface is a plane, the equation must be linear; in addition, for fixed y and varying x , the corresponding value of z stays constant. So the equation must depend only on y and z . To determine the equation precisely, we thus look at the trace of the surface on the yzplane as shown in Consequently, the linear equation is y + z = 1 . 004 10.0 points A line ℓ passes through the point P (4 , 4 , 4) and is parallel to the vector ( 1 , 3 , 4 ) . At what point Q does ℓ intersect the xy plane? 1. Q (5 , 7 , 0) patino (mp25752) – Assignment5 – luecke – (57510) 3 2. Q (3 , 1 , 0) correct 3. Q (0 , 7 , 5) 4. Q (1 , 3 , 0) 5. Q (0 , 3 , 7) 6. Q (0 , 5 , 1) Explanation: Since the xyplane is given by z = 0, we have to find an equation for ℓ and then set z = 0....
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 Spring '09
 Lueke

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