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# 13.4 Vectors - PowerPoint PPT Presentation

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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Presentation Transcript

B

A

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

• Vectors have

• Direction

• Magnitude (Length, Distance)

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

A

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)

• 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?

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

A

AB = (5, 2)

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

• 3 AB

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

• -2 AB

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

• -2 AB

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

PQ + QR = PR

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

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 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 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 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

B

C

A

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