Gilbert_Hmwk10sol

Gilbert_Hmwk10sol - moseley(cmm3869 – HW10 – Gilbert...

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Unformatted text preview: moseley (cmm3869) – 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 parallel to a third line are parallel , III. two lines perpendicular to a plane are parallel . 1. all of them 2. I only 3. II only 4. I and II only 5. III only 6. II and III only correct 7. none of them 8. I and 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: each of the two lines has a direc- tion vector parallel to the direction vector of the third line, so must be scalar multiples of each other. III. 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. 002 10.0 points Which of the following surfaces is the graph of 6 x + 4 y + 3 z = 12 in the first octant? 1. x y z 2. x y z correct 3. x y z 4. x y z moseley (cmm3869) – HW10 – Gilbert – (56380) 2 5. x y z 6. x y z 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 6 x + 4 y + 3 z = 12 . Now the x-intercept occurs at y = z = 0, i.e. at x = 2; similarly, the y-intercept is at y = 3, while the z-intercept is at z = 4. 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 , − 2 , 3) and parallel to the vector ( 2 , 1 , − 3 ) . 1. x = 2 + t, y = 1 − 2 t, z = − 3 + 3 t 2. x = 1 + 2 t, y = − 2 + t, z = 3 − 3 t correct 3. x = 1 − 2 t, y = 2 − t, z = 3 − 3 t 4. x = 2 + t, y = 1 + 2 t, z = 3 − 3 t 5. x = 2 − t, y = − 1 + 2 t, z = − 3 + 3 t 6. x = − 1 + 2 t, y = 2 + t, z = − 3 − 3 t Explanation: A line passing through a point P ( a, b, c ) and having direction vector v is given para- metrically by r ( t ) =...
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This note was uploaded on 04/12/2011 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas.

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Gilbert_Hmwk10sol - moseley(cmm3869 – HW10 – Gilbert...

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