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.

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.

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.

Lines in space

Lines in space

Lines in space

Lines in space

Lines in space

Lines in space

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

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.

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

Equations of PLANES in space.

Different ways to specify a plane:

Equations of PLANES in space.

1. Give three non-co-linear points.

Different ways to specify a plane:

Equations of PLANES in space.

1. Give three non-co-linear points.

Different ways to specify a plane:

Equations of PLANES in space.

2. Give two non-parallel intersecting lines.

Different ways to specify a plane:

Equations of PLANES in space.

2. Give two non-parallel intersecting lines.

Different ways to specify a plane:

Equations of PLANES in space.

Different ways to specify a plane: