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# Calculus II - 31

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Stewart Calculus 12.1

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• ### Calculus II - 31

1. 1. 12.1 3D coordinate systems z (a,b,c) c o b x a y
2. 2. What is the meaning of the followingequation in R ? = = = + + =
3. 3. Distance formula in 3D space:The distance between ( , , ) and ( , , ) is | |= ( ) +( ) +( )An equation of a sphere with center ( , , ) andradius is ( ) +( ) +( ) =
4. 4. 12.2 VectorsA vector is a quantity that has bothmagnitude and direction. B = AThe zero vector has no specific direction.
5. 5. D B v u CA
6. 6. D B v u = C =A
7. 7. D B v u = C =A u
8. 8. D B v u = C =A 2u u
9. 9. D B v u = C =A 2u u u/2
10. 10. D B v u = C =A 2u u -u u/2
11. 11. Vector Addition v u
12. 12. Vector Addition and Subtraction v u u v
13. 13. Vector Addition and Subtraction v u u v The Triangle Law u+v
14. 14. Vector Addition and Subtraction v u u v The Triangle Law u+v u v
15. 15. Vector Addition and Subtraction v u u v The Triangle Law u+v u v
16. 16. Vector Addition and Subtraction v u u v The Triangle Law u+v u u+v The Parallelogram Law v
17. 17. Vector Subtraction v u
18. 18. Vector Subtraction v = +( ) u
19. 19. Vector Subtraction v = +( ) u -v u
20. 20. Vector Subtraction v = +( ) u -v u-v u
21. 21. Properties of vectors: , , are vectors, , are scalars. + = + +( + )=( + )+ + = +( )= ( + )= + ( + ) = + ( ) = ( ) =