5Bmidterm-2007-solution

5Bmidterm-2007-solution - Midterm Exam Math 5B November...

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Unformatted text preview: Midterm Exam Math 5B November 2007 Your name: Your perm. #: Your signature: 1. 2. Subtotal: 3. 4. Subtotal: Total (100): When presenting your solutions, be sure to write down all the steps clearly and cleanly! If you dont show work, and only write down your final result for a problem, youll receive no credit for that problem! 1 1. (25 points) Let P be the plane which contains the points A = (1 , 2 , 1) ,B = (2 , 1 , 2) and C = (2 , 3 , 4). (1) Find a normal vector to P . (2) Find an equation for P . (3) Find the area of the triangle with A,B and C as the vertices. (Hint: consider a suitable parallelogram.) Solution (1) We have- AB = (2- 1 , 1- 2 , 2- 1) = (1 ,- 1 , 1) , (1)- AC = (2- 1 , 3- 2 , 4- 1) = (1 , 1 , 3) . (2) Then a desired normal vector is given by- AB - AC . There holds- AB - AC = i j k 1- 1 1 1 1 3 =- 4 i- 2 j + 2 k . (3) 2) We have the normal vector given above. We take A as the reference point....
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5Bmidterm-2007-solution - Midterm Exam Math 5B November...

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