Calculus II/Test 4

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Wright State University Lake Campus/2017-1/MTH2310 ... (log)

If we follow the previous course, Test 4 might include material on the power series.

  • All the examples in Chapter 9.1 might be on the test (pp634-38)
  • wikipedia:Dot product wikipedia:Cross product
  • Vectors let's look at rotations.--Guy vandegrift (discusscontribs) 16:56, 5 April 2017 (UTC)
  • These examples from Chapter 9 look like good candidates for Test 4:
    • Example 1 p664: Find the equation of a line (in x,y,z coordinates) in a given direction through a given point.
    • Example 2 p665: Find the equation of a line (in x,y,z coordinates) through two points.
    • Example 4 p667: Find the equation of a plane perpendicular to a given direction, passing through a given point.
  • Polar coordinates Appendix H page A55
    • Examples 2-5 are easy and at least one of these will be on the test.
    • Example 6 is moderately difficult and will be on the test in one form or another.
    • The whole class stopped at A58 and nothing on or after Example 7 will be covered.

Example 8 Challenge question "extra credit' and not a lot of it.[edit | edit source]

Here the dotted line is the plane, and the normal is B, and r1r0 is A. The point r1 is tail vector A.

See p669 of textbook: Find the distance from a point to given a plane, if the plane is defined as follows:

is some point on the plane (i.e., three given numbers).
is normal to the plane (again, three given numbers).

Now draw the point and the plane in from a specific angle in which the given point and the normal lie in the plane of the paper (board), and use facts about dot-product. (I never bothered to define comp and proj as described on 652; I was familiar with comp but never heard of proj, but it is an easy concept to grasp if you understand this problem).

Rule: If, is a unit normal to the plane, then the magnitude of is the distance from the point to the plane. In the figure:
  1. is any vector connecting the point to somewhere on the plane (the calculated distance should not depend on ).
  2. The unit normal is given by:

If we view the expression in curly brackets as some constant, and drop the subscript "1", then we have the formula for a plane normal to .

Note that the distance, if because the point is already on the plane.