12CDE 12C: Vectors in the Plane 12D: The Magnitude of a Vector 12E: Operations with Plane Vectors

12C Vectors in the Plane In transformation geometry, translating a point a units in the x-direction and b units in the y-direction can be achieved using the translation vector 𝑎 𝑏 . 2 5 would be a vector two units in the x-direction and five units in the y-direction.

12C Continued i and j are examples of unit vectors because they have length 1. i = 1 0 and is a translation 1 unit in the positive x-direction. j = 0 1 and is a translation 1 unit in the positive y-direction.

12C Continued

12C different forms

12C continued

12C Example The vectors are equal even though they don’t have the same starting point.

12D: The Magnitude of a Vector Click to watch video: https://www.youtube.com/watch?v=bOIe0DIMbI8

12D Example

12D Unit Vectors A unit vector is any vector which has a length of one unit. Example:

12E Operations with Plane Vectors Algebraic Vector Addition I promise you can do this…check out the example on the next slide.

12E Vector Addition Example

12E Operations with Plane Vectors Algebraic Negative Vectors (add the opposite).

12E Operations with Plane Vectors Algebraic Negative Vectors (add the opposite). You can totally do this!

12E Operations with Plane Vectors Algebraic Negative Vectors (add the opposite). Example:

12E Operations with Plane Vectors Algebraic Scalar Multiplication – just multiply! Example:

12E Last Example!