234practice1 - Math 234 Practice Test#1 Show your work in...

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Unformatted text preview: Math 234, Practice Test #1 Show your work in all the problems. 1. Find parametric equations for the line in which the planes x +2 y + z = 1 and x − y + 2 z = − 8 intersect. 2. Compute the distance from the point (2 , 2 , 3) to the plane through the points A = (0 , , 0), B = (2 , , − 1) and C = (2 , − 1 , 0). 3. Compute the area of the parallelogram with three of its vertices given by A = (2 , − 2 , 1) , B = (3 , − 1 , 2) and C = (3 , − 1 , 1) 4. (Cancellation in a dot product ?) Let u , v , w be three vectors with u negationslash = 0. Is it true that u • v = u • w implies v = w ? If you think it is true explain why, otherwise provide a counterexample. 5. Sketch the surface given by the equation z = 1 − x 2 . 6. Describe the given sets with a single equation or a pair of equations: The circle of radius 1 centered at ( − 3 , 4 , 1) and lying in a plane parallel to the (a) xy-plane (b) yz-plane (c) xz-plane 1 Solutions 1. Normal vectors of the two planes are given by n 1 = (1 , 2 , 1) and n 2 = (1 , − 1 , 2) respectively. The line of intersection is perpendicular to both n 1 and n 2 . The following vector is then parallel to the line of intersection:....
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This note was uploaded on 12/11/2010 for the course MTH 234 taught by Professor Irinakadyrova during the Spring '10 term at Michigan State University.

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234practice1 - Math 234 Practice Test#1 Show your work in...

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