1. Discrete Math Section 12.5 Apply vectors in three dimensions
Given points A(x1,y1,z1) and B(x2,y2,z2)
Vector = <x2-x1, y2-y1, z2-z1>
Absolute value of = √((x2 – x1)2 + (y2 – y1)2 + (z2 – z1)2 )
Midpoint of = (x2 + x1 , y2 + y1 , z2 + z1)
Equation of sphere (x – x1)2 + (y – y1)2 + (z – z1)2 =r2
center at (x1, y1, z1) radius = r
Vector Equation (x,y,z) = (x0,y0,z0) + t<a,b,c>
Dot product x1x2 + y1y2 + z1z2

2. Add the vectors <2,7,-1> and <-6,1,4>
Examples
Add the vectors <2,7,-1> and <-6,1,4>
Find the absolute value of V = <4,1,6>

3. If v = <6,2,0> and u = <1,-1,8> find v∙u
Find a vector equation through (7,4,2) and parallel to (x,y,z) = (1,0,-2) + t<4,8,3>

4. Find the parametric equations of
(x,y,z) = (4,5,-1) + t<3,-2,0>
Find the angle between the vectors <3,-5,2> and <0,1,4>

5. A sphere has points A(8,-2,3) and B(4,0,7) as endpoints of a diameter
A sphere has points A(8,-2,3) and B(4,0,7) as endpoints of a diameter. a. Find the center C and the radius r of the sphere. b. Find the equation of the sphere. c. Where does a particle with the vector equation (x,y,z) = (5,2,7) + t<0,-4,3> intersect the sphere?

6. Assignment
Page 450
Problems 2,4,8,9,12,16,22,24,26,28,42,43