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Vector Multiplication Reminder

Module by: Paul Padley

Summary: 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 ⃗ 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 ⃗ = A x B x + A y B y + A z B z

A ⃗ × B ⃗ 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 ( 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 ⃗ A ⃗ × A ⃗

Answer: 0

What is A ⃗ ⋅ ( A ⃗ × B ⃗ ) A ⃗ ⋅ ( A ⃗ × B ⃗ )

Answer: 0

Another useful thing to remember A ⃗ ⋅ ( B ⃗ × C ⃗ ) = ( A ⃗ × B ⃗ ) ⋅ C ⃗ A ⃗ ⋅ ( B ⃗ × C ⃗ ) = ( A ⃗ × B ⃗ ) ⋅ C ⃗ = ( C ⃗ × A ⃗ ) ⋅ B ⃗ = ( C ⃗ × A ⃗ ) ⋅ B ⃗ This is the scalar triple product which is the volume of a parallelopiped whose edges are given by A ⃗ , B ⃗ , C ⃗ A ⃗ , B ⃗ , C ⃗ .

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