Precalculus – MAT 129. Instructor: Rachel Graham Location: BETTS Rm. 107 Time: 8 – 11:20 a.m. MWF. Chapter Ten. Analytic Geometry in Three Dimensions. Ch. 10 Overview. The Three-Dimensional Coordinate System Vectors in Space The Cross Product of Two Vectors Lines and Planes in Space.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Instructor: Rachel Graham
Location: BETTS Rm. 107
Time: 8 – 11:20 a.m. MWF
Analytic Geometry in Three Dimensions
This text book uses a right-handed system approach.
Figure 10.1 on pg. 742 shows a diagram of this orientation.
Note the three planes: xy, xz, and zy
The distance between the points (x1, y1, z1) and (x2, y2, z2) is given by the formula:
The Midpoint formula is given by:
The standard equation of a sphere with center (h,k,j) and radius = r is given by:
(x – h)2 + (y – k)2 + (z – j)2 = r2
Pg. 745 Examples 4 & 5
These are the two ways I want you to know how to do these.
1. Find the standard equation of a sphere with center (-6, -4, 7) and intersecting the y-axis at (0, 3, 0).
2. Find the center and radius of the sphere given by: .
x2 + y2 + z2 - 6x + 12y + 10z + 52 = 0
Standard form: v = v1i + v2j + v3k
Component form: v = <v1,v2,v3>
See all of the properties in the blue box on page 750.
Write the vector v = 2j – 6k in component form.
<0, 2, -6>
If Θ is the angle between two nonzero vectors u and v, then
cos Θ = u ∙ v / ||u|| ||v||
Pg. 752 Example 3
Simply following the formulas will be all you need to do.
Two vectors are parallel when one is just a multiple of the other.
Pg. 752 Example 4
If two line segments are connected by a point and are parallel you can conclude that they are collinear points.
Pg. 753 Example 5
To find the cross product of two vectors you do the same steps as if you were finding the determinant of a matrix.
Note the algebraic properties of cross products in the blue box on pg. 757.
Pg. 758 Example 1
You want to leave it in i, j, k form.
See the blue box on pg 759.
note: orthogonal means perpendicular.
Pg. 759 Example 2
This is the kind of thing you will have to do again.
When we move up a dimension we get to a triple scalar product which is a combination of the stuff that we have learned so far.
See the blue boxes on pg. 761.
Pg. 761 Example 4
Pay close attention! As you should remember from determinants, these can be tricky.