Your SlideShare is downloading. ×
  • Like
Calculus II - 32
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×

Now you can save presentations on your phone or tablet

Available for both IPhone and Android

Text the download link to your phone

Standard text messaging rates apply

Calculus II - 32

  • 300 views
Published

Stewart Calculus 12.2

Stewart Calculus 12.2

  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
No Downloads

Views

Total Views
300
On SlideShare
0
From Embeds
0
Number of Embeds
0

Actions

Shares
Downloads
11
Comments
0
Likes
1

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n

Transcript

  • 1. 12.2 VectorsA vector is a quantity that has bothmagnitude and direction. B = AThe zero vector has no specific direction.
  • 2. 3D coordinate system: z (a,b,c) c o b x a y
  • 3. 3D coordinate system: z (a,b,c) (a,b,c) c o b x a y
  • 4. Given points ( , , ) and ( , , ),the vector = , , z (x2,y2,z2) (x2-x1,y2-y1,z2-z1) (x1,y1,z1) o x y
  • 5. Given points ( , , ) and ( , , ),the vector = , , z (x2,y2,z2) (x2-x1,y2-y1,z2-z1) (x1,y1,z1) o x y ! o r 2D Sim ilar f
  • 6. The addition, subtraction and scalarmultiplication: , , + , , = + , + , + , , , , = , , , , = , ,The length of the vector = , , is | |= + +Unitizing a vector: = | |
  • 7. The addition, subtraction and scalarmultiplication: , , + , , = + , + , + , , , , = , , , , = , ,The length of the vector = , , is | |= + + ! o r 2DUnitizing a vector: Sim ilar f = | |
  • 8. zStandard basis vectors: (a,b,c) = , , k = , , i o j x = , , y , , = + +
  • 9. zStandard basis vectors: (a,b,c) = , , k = , , i o j x = , , y , , = + + ! o r 2D Sim ilar f
  • 10. The dot product (or inner product) of = , , and = , , is given by · = + +It can also be defined for 2D vectors.The cross product of = , , and = , , is given by = , ,It can only be defined for 3D vectors.
  • 11. = , ,
  • 12. = , ,== +
  • 13. = , , = = +Determinant of order 2: =