Geometric Vectors

8-1

What is a vector?

• Suppose we are both traveling 65mph on Highway 169 and we pass each other going opposite directions. I’m heading back from Tulsa and you are heading to Tulsa. Describe our vectors.

Vector Definition

• A quantity that has both a magnitude and a direction.

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“u” would be considered the magnitude here.

uA

B

Look at the example on the board…

• We have vector PQ, what is its magnitude?

• Absolute value bars are often used.

Standard Position

• If a vector has an initial point at the origin, we consider it to be in standard position.

• The direction of a vector in standard position is given by the angle created between the positive x-axis and the vector…

• Let’s make a 115 degree vector “r”

Zero Vector

• Draw the zero vector in standard position.

Your turn…

• Someone come up to the board and make a 4 inch 45 degree vector.

What would make two vectors equal?

Your turn…

• Draw two vectors that have the same magnitude but different directions.

• Draw to vectors that are equal.

Can we sum vectors?

• What should we consider when summing a vector?

2 Methods for Summing Vectors

• 1. Parallelogram Method

• 2. Triangle (Tip to Tail) method.

• We refer to the sums as “resultant vectors”

Ok, let’s add some vectors…

• 1 student draw a vector

• 1 student draw another vector

• 1 student add the vectors

What is an opposite vector?

What are parallel vectors?

Definition

• We often refer to the two vectors used for a sum of vectors as the “components” of the resultant vector… For example…

Definition

• Scalar Quantity: A quantity with only a magnitude.

• Give me some examples of scalar quantities.

Let’s practice some…

• #14, #15, #16, #17, #21, #25, #31