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MA242.003

MA242.003. Day 7 – January 15, 2013 Review: Dot and Cross Products Section 9.5 – Lines and Planes. Review of Dot and Cross Products. Review of Dot and Cross Products. 9.4: Lines and Planes. This semester we will study curves and curved surfaces . Here is an example in Maple.

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MA242.003

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  1. MA242.003 Day 7 – January 15, 2013 Review: Dot and Cross Products Section 9.5 – Lines and Planes

  2. Review of Dot and Cross Products

  3. Review of Dot and Cross Products

  4. 9.4: Lines and Planes This semester we will study curves and curved surfaces. Here is an example in Maple.

  5. 9.4: Lines and Planes This semester we will study curves and curved surfaces. Here is an example in Maple. So before studying curved surfaces we will study the simplest surfaces, namely planes.

  6. 9.4: Lines and Planes This semester we will study curves and curved surfaces. Here is an example in Maple. So before studying curved surfaces we will study the simplest surfaces, namely planes. Similarly before we study curves in space we will study the simplest curves, namely straight lines in space.

  7. Lines in space

  8. Lines in space

  9. Lines in space

  10. Lines in space

  11. Lines in space

  12. Lines in space

  13. 1. Note that any non-zero multiple of a direction vector is another direction vector so is not unique.

  14. 1. Note that any non-zero multiple of a direction vector is another direction vector so is not unique. 2. Note that there are infinitely many points on a line so P0 is not unique.

  15. NOTE: We will omit the discussion of “symmetric equations of a line” and work only with parametric equations of lines.

  16. Equations of PLANES in space. Different ways to specify a plane:

  17. Equations of PLANES in space. Different ways to specify a plane: 1. Give three non-co-linear points.

  18. Equations of PLANES in space. Different ways to specify a plane: 1. Give three non-co-linear points.

  19. Equations of PLANES in space. Different ways to specify a plane: 2. Give two non-parallel intersecting lines.

  20. Equations of PLANES in space. Different ways to specify a plane: 2. Give two non-parallel intersecting lines.

  21. Equations of PLANES in space. Different ways to specify a plane:

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