13 4 vectors
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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.

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13.4 Vectors

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13 4 vectors

13.4 Vectors


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

  • Vectors have

    • Direction

    • Magnitude (Length, Distance)


Ab change in x change in y

B

A

AB = (change in x, change in y)


Ab change in x change in y1

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

A

AB = (5, 2)


Magnitude of vector ab

Magnitude of vector AB

  • |AB|

  • The length of the arrow

  • Use Pythagorean Theorem or the Distance formula.


Scalar multiples

Scalar Multiples

  • 3 AB


Scalar multiples1

Scalar Multiples

  • -2 AB


Scalar multiples2

Scalar Multiples

  • -2 AB


White board practice

White Board Practice

  • 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

  • Given points P(-1,-5) and Q(5,3)

    • Sketch PQ

    • Find PQ

    • Find |PQ|

    • Find 3PQ

    • Find -2PQ


Equal vectors

Equal Vectors

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


Vector sums

Vector Sums

  • To add 2 vectors

    PQ + QR = PR

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


Definition

Definition

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

Two vectors are equal if they have the same

distance and direction.

u

=

AB

B

u

A


Opposite vectors

Opposite Vectors

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(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(subtracting)

D

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

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

C

-(CD)

B

-(CD)

A

AD


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