222-robbin-07spex04

222-robbin-07spex04 - Name _________ __ 323 324 326 327 328...

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Unformatted text preview: Name _________ __ 323 324 326 327 328 329 330 331 Math ‘222, Exam IV, Monday April 30, 2007 Circle your section: 113 INGRAHAM B329 VAN VLECK B135 VAN VLECK 119 VAN VLECK B337 VAN VLECK B305 VAN VLECK B329 VAN VLECK B333 VAN VLECK TR 08:50—09:40 TR 09:55—10:45 TR 11:00—11:50 TR 11:00—11:50 TR 12:05—12:55 TR 13:20~14:10 TR 14:25—15:15 TR 152304620 I I I I Georgiou, Nicos Georgiou, Nicos Ache, Antonio Beros, Achilles Ache, Antonio Beros, Constantinos Beros, Constantinos Beros, Achilles W SHOW YOUR REASONING. I. (30 points.) Find parametric equations for the line through the points A(3, 0, 1), B (2, 1, 2). (2) Find the point on this line which is closest to the origin. II. (30 points.) (1) Find a, b, c so that axl + bxz + 0533 = 1 is the equation of the plane containing the points A(3,0, 1), B(27 1, 2), C(0,4,0). (2) Find the distance from the origin to this plane. p—u—u—I > find {13, g?) for which III. (30 points.) Given the vectors 3, = ( g ) and I; = ( a = e +37, with 51113, g .L 5. (Here :‘n’ means the vectors are parallel and 1') .L 3 means the vector are orthogonal.) IV. (30 points.) True or False: If 6, x 3 = E x 3 and 3 sé 5 then 6 = Z? (Note: True means always true. If the assertion is true, prove it; if false illustrate with an example.) V. (30 points.) There are three points X ($1,532,333) such that the four points A(3,0,1), B(2, 1, 2), C(0, 4, 0), and X are the vertices of a parallelogram. Find these three points and the area of each parallelogram. ...
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This note was uploaded on 08/08/2008 for the course MATH 222 taught by Professor Wilson during the Fall '08 term at Wisconsin.

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222-robbin-07spex04 - Name _________ __ 323 324 326 327 328...

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