Cross Product
Cross Product
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In This Presentation...
? We will give a definition ? Look at the properties ? Do some examples
Cross Product
Definition: If a = and b = , then the cross product of a and b is the vector,
a x b = = (a2b3 ? a3b2)i + (a3b1 ? a1b3)j + (a1b2 ? a2b1)k
Cross Product
Note the result is a vector and NOT a scalar value. For this reason, it is also called the vector product.
To make this definition easer to remember, we usually use determinants to calculate the cross product.
Determinants
? Determinant of order 2:
? Determinant of order 3:
Cross Product
We can now rewrite the definition for the cross product using these determinants:
If you perform the determinants, you will obtain exactly what was stated in the definition.
Orthogonal Vectors
When you take the cross product of two vectors a and b, The resultant vector, (a x b), is orthogonal to BOTH a and b. We can use the right hand rule to determine the direction of a x b
Parallel Vectors
Two nonzero vectors a and b are parallel if and only if, a x b = 0
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