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12.1 3D coordinate      systems               z                   (a,b,c)                   c           o       b         ...
What is the meaning of the followingequation in R ?    =     =     =      +    +    =
Distance formula in 3D space:The distance between      ( ,   ,   )   and    ( ,       ,   )   is   |    |=    (          )...
12.2 VectorsA vector is a quantity that has bothmagnitude and direction.                            B                     ...
D        B                v    u            CA
D        B                v    u                   =            C                        =A
D            B                    v        u                   =                C                            =A    u
D            B                         v        u                        =                C                               ...
D            B                         v        u                          =                C                             ...
D            B                         v        u                          =                C                             ...
Vector Addition                  v       u
Vector Addition and Subtraction                  v         u     u       v
Vector Addition and Subtraction                   v         u     u         v       The Triangle Law             u+v
Vector Addition and Subtraction                    v          u     u          v       The Triangle Law              u+v  ...
Vector Addition and Subtraction                    v          u     u          v       The Triangle Law              u+v  ...
Vector Addition and Subtraction                    v          u     u          v       The Triangle Law              u+v  ...
Vector Subtraction                     v       u
Vector Subtraction                     v   =   +(   )       u
Vector Subtraction                     v       =   +(   )       u                -v                         u
Vector Subtraction                      v       =   +(   )       u                 -v           u-v                       ...
Properties of vectors:  , ,   are vectors,     ,   are scalars.   + = +   +( + )=( + )+   +    =   +(       )=  ( + )=    ...
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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. + = + +( + )=( + )+ + = +( )= ( + )= + ( + ) = + ( ) = ( ) =

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