13 4 vectors
Download
1 / 19

13.4 Vectors - PowerPoint PPT Presentation


  • 58 Views
  • Uploaded on

13.4 Vectors. When a boat moves from point A to point B, it’s journey can be represented by drawing an arrow from A to B. AB Read vector AB. B. A. Vectors. Vectors have Direction Magnitude (Length, Distance). B. A. AB = (change in x, change in y). B. A.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' 13.4 Vectors' - vladimir-valenzuela


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

B

A


Vectors
Vectors can be represented by drawing an arrow from A to B.

  • Vectors have

    • Direction

    • Magnitude (Length, Distance)


Ab change in x change in y

B can be represented by drawing an arrow from A to B.

A

AB = (change in x, change in y)


Ab change in x change in y1

B can be represented by drawing an arrow from A to B.

A

AB = (change in x, change in y)

  • Going from point A to point B

    • How much is there a change in the x direction?

    • How much is there a change in the y direction?


Ab 5 2

B can be represented by drawing an arrow from A to B.

A

AB = (5, 2)


Magnitude of vector ab
Magnitude of vector AB can be represented by drawing an arrow from A to B.

  • |AB|

  • The length of the arrow

  • Use Pythagorean Theorem or the Distance formula.


Scalar multiples
Scalar Multiples can be represented by drawing an arrow from A to B.

  • 3 AB


Scalar multiples1
Scalar Multiples can be represented by drawing an arrow from A to B.

  • -2 AB


Scalar multiples2
Scalar Multiples can be represented by drawing an arrow from A to B.

  • -2 AB


White board practice
White Board Practice can be represented by drawing an arrow from A to B.

  • Given points P(-3,4) and Q(-2,-2)

    • Sketch PQ

    • Find PQ

    • Find |PQ|

    • Find 3PQ

    • Find -2PQ


White board practice1
White Board Practice can be represented by drawing an arrow from A to B.

  • Given points P(-1,-5) and Q(5,3)

    • Sketch PQ

    • Find PQ

    • Find |PQ|

    • Find 3PQ

    • Find -2PQ


Equal vectors
Equal Vectors can be represented by drawing an arrow from A to B.

  • 2 vectors are equal if they have the same magnitude and the same direction


Vector sums
Vector Sums can be represented by drawing an arrow from A to B.

  • To add 2 vectors

    PQ + QR = PR

    (4,1)+(2,3) = (6,4)


Definition
Definition can be represented by drawing an arrow from A to B.

A vector is defined to be a directed line segment. It

has both direction and magnitude (distance). It

may be named by a bold-faced lower-case letter or

by the two points forming it - the initial point and

the terminal point. Examples: u or AB

B

u

A


Equal vectors1
Equal Vectors can be represented by drawing an arrow from A to B.

Two vectors are equal if they have the same

distance and direction.

u

=

AB

B

u

A


Opposite vectors
Opposite Vectors can be represented by drawing an arrow from A to B.

Opposite vectors have the same magnitude, but opposite directions. That is, the terminal point of one is the initial point of the other.

u

-u


Resultant vectors adding
Resultant Vectors can be represented by drawing an arrow from A to B.(adding)

When vectors are added or subtracted, the sums or differences are called resultant vectors.

Geometrically, we add vectors by placing the initial point of the second vector at the terminal point of the first vector in a parallel direction. The resultant vector has the initial point of vector 1 and the terminal point of the displaced vector 2.

D

B

A

C

D

AB + CD = AD

B

C

A


Resultant vectors subtracting
Resultant Vectors can be represented by drawing an arrow from A to B.(subtracting)

D

We subtract a vector the algebraic way by adding the opposite.

AB - CD = AB + (-CD)=AD

C

-(CD)

B

-(CD)

A

AD


ad