Warm up:• Draw a vector on the Cartesian coordinate

plane, and describe this vector in words.

Vectors Two and Three Dimensions

Section 6.5

Describing Vectors in 2D• Using the Cartesian coordinates, draw the vector

OA[2, 3] and OB[-4, 5].

Describing Vectors in 2D• Using the Cartesian coordinates, draw the vector

OA[2, 3] and OB[-4, 5].

Try: Write vector AB in terms of OA and OB:

Problem: Describe the following vectors in terms of other vectors

from the origin:• a) Vector AB:

• b) Vector BA:

• c) Vector - AB

Drawing Points in 3-Space

• Plot the point (3, 2, 4) in 3D space:

Drawing Points in 3-Space

• Plot the point (3, 2, 4) in 3D space:

Practice:

• Try to plot the following vector using a prism:

[-2, 4, 3]

Coordinates in 3D (R3)

• Determine the coordinates of the following points:

- Point A:

- Point B:

- Point C:

Equation of a Plane

• Write the coordinates of each point, and explain what is the same about them:

- Point A, B, and F

Equation of a Plane

• Write the coordinates of each point, and explain what is the same about them:

- Point A, B, and F

- Point C, D, and E:

Summary:

• In general what is the sum of vector AB + BC?

• Why can we name a vector using only one point?

• What is the right hand rule?

Practice: Pg. 316, #1-10, 14, 17, 19