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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 have
- Direction
- Magnitude (Length, Distance)

B

A

B

A

- 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|
- The length of the arrow
- Use Pythagorean Theorem or the Distance formula.

- 3 AB

- -2 AB

- -2 AB

- Given points P(-3,4) and Q(-2,-2)
- Sketch PQ
- Find PQ
- Find |PQ|
- Find 3PQ
- Find -2PQ

- Given points P(-1,-5) and Q(5,3)
- Sketch PQ
- Find PQ
- Find |PQ|
- Find 3PQ
- Find -2PQ

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

- To add 2 vectors
PQ + QR = PR

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

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

Two vectors are equal if they have the same

distance and direction.

u

=

AB

B

u

A

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

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

D

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

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

C

-(CD)

B

-(CD)

A

AD