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272Finalconcept

# 272Finalconcept - Mat 272 Calculus III Final Exam on May 3...

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Mat 272 Calculus III Dr. Firoz Final Exam on May 3, 2008 Saturday at 7:40 in EDC 117 Test Concept 1. Distance formula 2 2 1 2 2 1 2 2 1 2 1 ) ( ) ( ) ( z z y y x x P P D - + - + - = = 2. Equation of a sphere 2 2 2 2 ) ( ) ( ) ( r c z b y a x = - + - + - center at ( a , b , c ) radius r 3. Identify and plot the region 2 2 2 2 ) ( ) ( ) ( r c z b y a x - + - + - 4. Finding center and radius from the equation of the sphere 0 2 2 2 2 2 2 = + + + + + + d hz gy fx z y x 5. Equation of a line segment in vector form tv r r + = 0 , where > =< > =< c b a v z y x r t , , , , , , 0 0 0 0 , where v is a direction vector 6. Also identify the vector equation 1 0 , ) 1 ( 1 0 + - = t tr r t r 7. The dot and cross product of two vectors 3 3 2 2 1 1 cos b a b a b a B A B A + + = = θ sin , 3 2 1 3 2 1 B A B A b b b a a a k j i B A = × = × 8. Direction cosines and direction numbers 9. Work done by a force to move an object from a point P to a point Q is cos D F

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272Finalconcept - Mat 272 Calculus III Final Exam on May 3...

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