1. Dr. Shildneck

2. Dot Product Again, there are two types of Vector Multiplication. The inner product,called the Dot Product, and the outer product called the Cross Product. The Dot Product is a scalar (number).

3. Using the Alternate Formula for Dot Product Find the angle between vectors v = and w =

4. Cross Product The result of performing the Cross Product of two vectors is actually another vector. The vector created by the cross product is the vector orthogonal (perpendicular) to the plane that contains the two vectors. A x B, which is read “A cross B,” is the vector that is orthogonal to both A and B.

5. Cross Product The definition for the Cross Product is described here. If a = a 1 i + a 2 j + a 3 k and b = b 1 i + b 2 j + b 3 k, the cross product is defined as a x b = (a 2 b 3 – a 3 b 2 )i – (a 1 b 3 – a 3 b 1 )j + (a 1 b 2 – a 2 b 1 )k As difficult as this pattern seems, we can re-write it more Simply in “determinant form” involving i, j, and k and the components of a and b.

6. Determinant form of the Cross Product The determinant form for the Cross Product of a and b is a x b =

7. Using the Determinant Form of Cross Product Find vector orthogonal to both v = and w = v x w =

8. ASSIGNMENT YOUR Text. Regular Text (p. 522 #1-7, 11-21, 37-41, 45-49 (odds only)