# A4 - x + y + z = 5 and 3 x-y = 4 . Problem 1.5. Sketch the...

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MATH 222 HOMEWORK 4 DUE OCTOBER 11, 2011 October 10 is a holiday. The assignment is due by 5PM on October 11. Rogers Section - Drop off the assignment outside the door of 1243 Burnside Hall. Loveys Section - Drop off the assignment outside the door of 916 Burnside Hall. 1. P ROBLEMS Problem 1.1. Find a parametric form for the line 3 x - 2 2 = 4 - y = z + 3 2 Problem 1.2. Find the area of the triangle formed by the lines 1 : (1 , 1 , 2) t + (0 , 1 , 2) , 2 : ( - 3 , 3 , 6) s + ( - 1 , 6 , 12) , and the x -axis. Problem 1.3. Find the equation of a plane tangent to the sphere x 2 + y 2 + z 2 - 6 x - 2 y - 4 z + 9 = 0 , at the point (4 , 1 , 0) . Problem 1.4. Find an equation of the plane that passes through the points (1 , 0 , - 1) and (2 , 1 , 0) , and is parallel to the line of intersection of the planes
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Unformatted text preview: x + y + z = 5 and 3 x-y = 4 . Problem 1.5. Sketch the surface given by y = 2 x + x 2 + z 2 . Then nd a parametric formula describing the curve of intersection with the plane 2 x-y + 2 z =-1 Problem 1.6. The position of a particle is given by x ( t ) = (ln( t ) , ln(2-t 2 ) , 1 + 2 t + 3 t 5 ) . Calculate the domain of x ( t ) . Find the velocity and acceleration vectors of the particle. What is the speed of the particle when t = 1 / 2 ? Problem 1.7. Let r ( t ) = ( t 2 + t,t + 3 ,t 3-t 2 + t-1) . Calculate R 1 r ( t ) d t . 1...
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## This note was uploaded on 01/11/2012 for the course MATH 100 taught by Professor Loveys during the Fall '11 term at McGill.

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