Section 11.4 The Cross Product Calculus III September 22, 2009 Berkley High School.

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Presentation transcript:

Section 11.4 The Cross Product Calculus III September 22, 2009 Berkley High School

2 Operations on Vectors (So Far) Scalar Multiplication Vector Addition Vector Subtraction Dot Product

3 New Operation: Cross Product

4 Definition of Determinant

5

6 Definition of Cross Product

7 Example

8

9 Properties: Direction & Magnitude

10 Properties: Direction & Magnitude

11 Properties: Area of Parallelogram

12 Properties

13 Assignment Section 11.4, 1-35, odd x25 But wait, there’s more…

14 Volume of Parallelepiped

15 Volume of Parallelepiped

16 Volume of Parallelepiped

17 Volume of Parallelepiped

18 Volume of Parallelepiped

19 Volume of Parallelepiped

20 Volume of Parallelepiped Triple Scalar Product

21 Example

22 Example

23 Are two vectors coplanar? Any two non-zero vectors define a plane. Are three vectors coplanar?  The vectors are coplanar iff the parallelepiped formed by the three vectors has Volume=0

24 Example

25 Are three points coplanar? Any three points define a plane. Are four points coplanar?  From the four points, three vectors can be formed with a common tail. If the vectors are coplanar, then the points are coplanar.

26 Assignment 11.4, odd