272Finalconcept

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/09/2008 for the course MAT 272 taught by Professor Firoz during the Spring '08 term at ASU.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online