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Vector Multiplication Reminder

Module by: Paul Padley. E-mail the author

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Summary: A three minute reminder of vector multiplication.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

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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