3D Vectors, Planes, and the Cross Product

1. VC.02: Day 2 3D Vectors, Planes, and the Cross Product

2. Review: Determinant of a 2 x 2 Matrix • Every square (n x n) matrix has a real number associated to it called the determinant • Short form:

3. Review: Determinant of a 3 x 3 Matrix • Method 2: Expansion by Minors

4. Example 5: Plane from Three Points

5. Defining the Cross Product

6. Defining the Cross Product

7. Defining the Cross Product

8. Defining the Cross Product

9. Defining the Cross Product

11. Summary: The Cross Product

12. Verifying the Cross Product We can verify that the cross product gives us a perpendicular vector to V and W for any choices of V and W. Try this in Mathematica: V={v1,v2,v3}; W={w1,w2,w3}; VxW=Cross[V,W]; Together[V.VxW] Together[W.VxW]

13. Example 6: The Cross Product

14. Example 5: Plane from Three Points (CONTINUED)

15. WE DID IT!!!!!!!!!!!!

16. Epilogue: The Magnitude of the Cross Product

17. Epilogue: The Magnitude of the Cross Product

18. Epilogue: The Magnitude of the Cross Product Answer Under the Box! ?