1. 11.2 Space coordinates and vectors in Space

2. 3 dimensional coordinate plane

3. Plotting points in 3D

4. 3D coordinate systems

5. The distance formula in 3-D

6. Example 1 Find the distance between points (2,-1,3) and (1,0,-2)

7. Example 1 Solution Find the distance between points (2,-1,3) and (1,0,-2)

8. Vectors in Space box

9. Equation of a sphere Find the equation of a sphere with Center(4,-1,1) and radius 7

11. Adding unit vectors (coordinates)

12. Find components of a vector by subtracting initial point from terminal point

14. Parallel vectors Vector w has initial point (2,-1,3) and terminal point (-4,7,5). Which of the following vectors is parallel to w? Why? u = (3,-4,-1) v= (-4,7,5)

15. Parallel vectors solution Parallel vectors are scalar multiples of each other (that is the definition of parallel) Vector u is parallel to the given vector because -2 times vector u equals the given vector

16. Example 5 Use vector to determine if the following points are collinear. P(1,-2,3), Q(2,1,0) and R(4,7,-6)

17. Example 5 Solution Use vector to determine if the following points are collinear. P(1,-2,3), Q(2,1,0) and R(4,7,-6)

18. Find a unit vector in the direction of v v = 3i + 2j + k Note: the TI 89 has this as a built in operation. Press 2 nd 5 math – 4 matrices – L vector ops- 1 unitV unitV([3,2,1])

19. For any job, it is important to have the right equipment. For this class you will need a TI89 Calculator