Vector multiplication.xhtml **new** 2005/07/01 11:23:01.643 GMT-5 2005/07/01 11:25:13.267 GMT-5 Paul Padley padley@rice.edu Paul Padley padley@rice.edu Vector Multiplication A three minute reminder of vector multiplication. It is presumed that you are familiar with vector multiplication. Here are some questions to ask yourself as a refresher: A ⃗ ⋅ B ⃗ . Is it a vector or a scalar? Answer: scalar A ⃗ ⋅ B ⃗ = A x B x + A y B y + A z B z A ⃗ × B ⃗ . Is it a vector or a scalar? Answer: Vector ( A ⃗ × B ⃗ ) x = A y B z − A z B y ( A ⃗ × B ⃗ ) y = A z B x − A x B z ( A ⃗ × B ⃗ ) z = A x B y − A y B x What is A ⃗ × A ⃗ Answer: 0 What is A ⃗ ⋅ ( A ⃗ × B ⃗ ) Answer: 0 Another useful thing to remember A ⃗ ⋅ ( B ⃗ × C ⃗ ) = ( A ⃗ × B ⃗ ) ⋅ C ⃗ = ( C ⃗ × A ⃗ ) ⋅ B ⃗ This is the scalar triple product which is the volume of a parallelopiped whose edges are given by A ⃗ , B ⃗ , C ⃗ .