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Unformatted text preview: rhodes (ajr2283) HW10 Gilbert (56380) 1 This print-out should have 10 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 planes perpendicular to a third plane are parallel , II. two lines perpendicular to a plane are parallel , III. two lines parallel to a third line are parallel . 1. all of them 2. I only 3. II and III only correct 4. II only 5. none of them 6. I and III only 7. I and II only 8. III only Explanation: I. FALSE: the xy-plane and yz-plane are both perpendicular to the xz-pane, but are perpendicular to eachh other, not parallel . 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 lines has a di- rection vector parallel to the direction vector of the third line, so must be scalar multiples of each other. 002 10.0 points Which of the following surfaces is the graph of 3 x + 6 y + 4 z = 12 in the first octant? 1. x y z 2. x y z correct 3. x y z 4. x y z rhodes (ajr2283) HW10 Gilbert (56380) 2 5. x y z 6. x y z Explanation: Since the equation is linear, its graph will be a plane. To determine which plane, we have only to compute the intercepts of 3 x + 6 y + 4 z = 12 . Now the x-intercept occurs at y = z = 0, i.e. at x = 4; similarly, the y-intercept is at y = 2, while the z-intercept is at z = 3. By inspection, therefore, the graph is x y z 003 10.0 points Find parametric equations for the line pass- ing through the point P (1 , 4 , 2) and parallel to the vector ( 2 , 2 , 1 ) . 1. x = 1 2 t, y = 4 2 t, z = 2 t 2. x = 1 + 2 t, y = 4 + 2 t, z = 2 t correct 3. x = 2 + t, y = 2 4 t, z = 1 + 2 t 4. x = 2 t, y = 2 + 4 t, z = 1 + 2 t 5. x = 2 + t, y = 2 + 4 t, z = 1 2 t 6. x = 1 + 2 t, y = 4 + 2 t, z = 2 t Explanation: A line passing through a point P ( a, b, c ) and having direction vector v is given para- metrically by...
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- Spring '07
- Multivariable Calculus