Thread: dot vs. cross

What is the purpose of the dot product as opposed to the purpose of the cross product?

Originally Posted by delgeezee

What is the purpose of the dot product as opposed to the purpose of the cross product?

the result of a dot product of two vectors is a scalar ...

work, a scalar quantity of energy, is the dot product of force and displacement vectors




the result of a cross product of two vectors is another vector ...

torque, a vector quantity, is the cross product of radius and force vectors




try a google search ... you'll find many more examples and applications.

Originally Posted by delgeezee

What is the purpose of the dot product as opposed to the purpose of the cross product?

There is a very simple answer and distinction between the two operations.
The dot product operation maps pairs of vectors to a scalar.
The cross product operation maps pairs of vectors to a vector.