12-6 Vectors

A vector is a mathematical object that has both magnitude (size) and direction

Students will be able to use basic vector operations and the dot product

Essential Understanding

Vector: has both magnitude and direction. Represented with an arrow

Magnitude: length of the arrow A vector has an initial point and terminal

point to determine direction If segments have the same magnitude they

can represent the same vector

Vocabulary

The initial point must be at the origin Complete a transformation of both points to

find the new terminal point in component form.

What are the component forms of the two vectors shown here?

(this makes it easier to determine the magnitude)

Component Form

Operations with vectors

Let u = <-2, 3> and v = <5, -2> What is |u + v| What is |u - v|

Adding and Subtracting

If the number is greater than 1, then only the magnitude changes

If the number is less than one, then the magnitude changes and the direction is reversed

Scalar Multiplication

Given u = <-2, 4> what is ◦ -u◦ 1/2u ◦ 3u

Scalar Multiplication

Multiplying two vectors together Expresses and angular relationship v = <v1, v2> and w = <w1, w2> Then the dot product is v1w1 + v2w2 If the dot product = 0, the two vectors are

normal, or perpendicular to each other.

Dot Product

Are the following vectors normal?<-2, 6>,<-9, -18>

<3, 5/6><-10/9, 4>

Finding the Dot Product

Pg. 813 #7 – 12, 20 – 34 even 14 problems

Homework