Download presentation
Presentation is loading. Please wait.
1
Section 11.4 The Cross Product Calculus III September 22, 2009 Berkley High School
2
2 Operations on Vectors (So Far) Scalar Multiplication Vector Addition Vector Subtraction Dot Product
3
3 New Operation: Cross Product
4
4 Definition of Determinant
5
5
6
6 Definition of Cross Product
7
7 Example
8
8
9
9 Properties: Direction & Magnitude
10
10 Properties: Direction & Magnitude
11
11 Properties: Area of Parallelogram
12
12 Properties
13
13 Assignment Section 11.4, 1-35, odd x25 But wait, there’s more…
14
14 Volume of Parallelepiped
15
15 Volume of Parallelepiped
16
16 Volume of Parallelepiped
17
17 Volume of Parallelepiped
18
18 Volume of Parallelepiped
19
19 Volume of Parallelepiped
20
20 Volume of Parallelepiped Triple Scalar Product
21
21 Example
22
22 Example
23
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
24 Example
25
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
26 Assignment 11.4, 41-47 odd
Similar presentations
