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3D Vectors, Planes, and the Cross Product

VC.02: Day 2. 3D Vectors, Planes, and the Cross Product. 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: . Review: Determinant of a 3 x 3 Matrix. Method 2: Expansion by Minors.

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3D Vectors, Planes, and the Cross Product

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  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

  10. Summary: The Cross Product

  11. 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]

  12. Example 6: The Cross Product

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

  14. WE DID IT!!!!!!!!!!!!

  15. Epilogue: The Magnitude of the Cross Product

  16. Epilogue: The Magnitude of the Cross Product

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

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