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Understanding Vectors in 2D and 3D Coordinate Systems

Explore vector representation on Cartesian planes in 2D and 3D dimensions. Learn to describe vectors, plot points, and solve problems using coordinates. Practice plotting vectors in 3D space and solving equations for points and planes. Enhance your understanding with exercises and examples.

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Understanding Vectors in 2D and 3D Coordinate Systems

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Presentation Transcript

  1. Warm up: • Draw a vector on the Cartesian coordinate plane, and describe this vector in words.

  2. Vectors Two and Three Dimensions Section 6.5

  3. Describing Vectors in 2D • Using the Cartesian coordinates, draw the vector OA[2, 3] and OB[-4, 5].

  4. 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:

  5. Problem: Describe the following vectors in terms of other vectors from the origin: • a) Vector AB: • b) Vector BA: • c) Vector - AB

  6. Drawing Points in 3-Space • Plot the point (3, 2, 4) in 3D space:

  7. Drawing Points in 3-Space • Plot the point (3, 2, 4) in 3D space:

  8. Practice: Try to plot the following vector using a prism: [-2, 4, 3]

  9. Determine the coordinates of the following points: Point A: Point B: Point C: Coordinates in 3D (R3)

  10. Write the coordinates of each point, and explain what is the same about them: Point A, B, and F Equation of a Plane

  11. Write the coordinates of each point, and explain what is the same about them: Point A, B, and F Point C, D, and E: Equation of a Plane

  12. 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

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