Cross Product Continuity: Showing Definition is Satisfied

[symbol0]

1. Show that the cross product is a continuous function

3.
I have tried to apply the definition of continuity: find a delta such that
|x-y|< delta implies |f(x)-f(y)|< epsilon
but I'm having trouble finding a delta that would take me to the conclusion.

 

[gabbagabbahey]

Perhaps you should show us what you've tried. What is |f(x)-f(y)| in this case?

 

[symbol0]

In this case, |f(x)-f(y)| is a real number (the length of a vector in R^3).
A better question is what is |x-y|. x is one pair of vectors in R^3 and y is another pair of vectors in R^3. Then what is |x-y|?
I have tried relating |x-y| to the fact that |a x b|=|a||b|sin(theta) but can't get anything that seems to be on the right direction.

 

[symbol0]

I figured it out.