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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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

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

A

AB = (5, 2)

Magnitude of vector AB

|AB|

The length of the arrow

Use Pythagorean Theorem or the Distance formula.

Scalar Multiples

3 AB

Scalar Multiples

-2 AB

Scalar Multiples

-2 AB

White Board Practice

Given points P(-3,4) and Q(-2,-2)

Sketch PQ

Find PQ

Find |PQ|

Find 3PQ

Find -2PQ

White Board Practice

Given points P(-1,-5) and Q(5,3)

Sketch PQ

Find PQ

Find |PQ|

Find 3PQ

Find -2PQ

Equal Vectors

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

Vector Sums

To add 2 vectors

PQ + QR = PR

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

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 Vectors

Two vectors are equal if they have the same

distance and direction.

u

=

AB

B

u

A

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)

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)

D

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