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

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.