Assignment 5 - patino (mp25752) – Assignment5 – luecke...

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Unformatted text preview: patino (mp25752) – Assignment5 – luecke – (57510) 1 This print-out should have 15 questions. Multiple-choice 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 3-space? 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 x-axis and y-axis are perpen- dicular, not parallel, yet both are perpendic- ular to the z-axis. 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 x-intercept occurs at y = z = 0, i.e. at x = 3; similarly, the y-intercept is at y = 4, while the z-intercept 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 yz-plane 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 xy-plane is given by z = 0, we have to find an equation for ℓ and then set z = 0....
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This note was uploaded on 10/21/2009 for the course M 53215 taught by Professor Lueke during the Spring '09 term at University of Texas.

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Assignment 5 - patino (mp25752) – Assignment5 – luecke...

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