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This **** is exam 1 from Spring 2007. Be aware that material covered by our first exam may be different --- we have covered some things that they did not, and they covered some things that we did not, at the same point in the quarter. Problems for material *NOT* covered by us have been crossed out. Use the Outcomes List as your primary resource for review for the exam; this exam is just being provided as an extra service *** Exam One MATH 200 Spring, 2007 Section____________ Name_______________________________ Show all your work on the exam paper, legibly and in detail, to receive full credit. There is no problem on page 8. Page 9 is extra credit. No Calculators. Page 1) 2) 3) 4) 5) 6) 7)_______9)_______ Total 1. (20 points) Find the vector component of v along b and the vector component of v orthogonal to b. v = 2i j + 3k , b = i + 2j + 2k Page 1 of 9 2. (20 points) Show that the lines L1 and L2 intersect and find their point of intersection. L1 : x = 2 + t , y = 2 + 3t , z = 3 + t L 2 : x = 2 + s , y = 3 + 4s , z = 4 + 2s Page 2 of 9 3. (20 points) Find the equation of the plane containing L1 and L2. L1 : x = 2 + t , y = 2 + 3t , z = 3 + t L 2 : x = 2 + s , y = 3 + 4s , z = 4 + 2s Page 3 of 9 4. (20 points) Find distance the from the point P( -3, 1, 2) to the line through the points A( 1, 1, 0) and B( -2, 3, -4). Page 4 of 9 5. (10 points) Sketch the traces of the ellipsoid xz planes. x2 y2 z2 + + = 1 in the xy , yz , and 9 16 4 Page 5 of 9 6 (5 points) Covert the point P( 4, / 6, 3) from cylindrical to rectangular coordinates. Page 6 of 9 7. (5 points) Covert the point P( 5, / 4, 2 / 3) from spherical to cylindrical coordinates. Page 7 of 9 Page 8 of 9 Extra Credit: Match the following equations with the graphs ON THE PREVIOUS PAGE. If there is no match, write "NO MATCH". (1 point each) x2 y2 z2 (8i) + - = 1 : _____________________________ 9 16 2 x2 y2 z2 (8ii) + + = 1 :______________________________ 9 9 9 x2 y z (8iii) + - = 1 :_______________________________ 9 16 2 x2 y2 z2 (8iv) + + = 1 :_________________________________ 9 16 4 x2 y2 z - - = 0 :_______________________________ (8v) 7 6 5 x y z (8vi) + - =1 :________________________________ 9 16 2 x2 y2 z2 (8vii) + + = 0 :________________________________ 9 16 4 x2 y2 z (8viii) + - = 0 :________________________________ 9 16 4 x2 y2 z2 (8ix) + - = 0 :_______________________________ 9 16 4 x2 y2 z2 (8x) + - = -1 :________________________________ 4 3 2 Page 9 of 9

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