#### Transcript of Precalc 6.3

**6.3-Vectors in the Plane**

**Any questions?**

This was only a short introduction to vectors. You will see a lot more in future Physics and Engineering classes. Now try these problems:

page 417- #1-12, 19-66, 71-73

Vector Basics

Intro to Vectors

Component Form

of a Vector

Example 1

**Ask them in class tomorrow!**

Vector Operations

Unit Vectors

Direction Angles

Vector Operations

Find the component form and magnitude of the vector v that has (1,7) as its initial point and (4,3) as its terminal point.

Example 2

Let u = <1,6> and v = <-4, 2> . Find

a. 3u

b. u + v

In many applications of vectors, it is useful to find a unit vector that has the same direction as a given vector v. To find a unit vector u, divide v by its length.

U is a scalar multiple of v. The vector u has a magnitude of 1 and the same direction of v. The vector u is called a unit vector in the direction of v.

Example 3

Find a unit vector in the direction of v=<-8,6>

Standard Unit Vectors

The unit vectors <1,0> and <0,1> are called the standard unit vectors and are denoted by i = <1,0> and

j = <0,1>.

Example 4 and 5

Ex. 4 - Let v = <-5, 3>. Write v as a linear combination of the standard unit vectors i and j.

Ex. 5 - Let v = 3i - 4j and w = 2i + 9j. Find v + w.

Ex. 4 - Let v = <-5, 3>. Write v as a linear combination of the standard unit vectors i and j.

v = -5i + 3j

Ex. 5 - Let v = 3i - 4j and w = 2i + 9j. Find v + w.

v + w = (3i +2i) + (-4j + 9j) = 5i + 5j

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