Understanding Continuity in the Cross Product Function

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1. Show that the cross product is a continuous function.

The Attempt at a Solution

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 making sense of what |x-y| is.
As I see it, x is a pairs of vectors in R^3 and so is y. Then what is |x-y|? and how do I get to the conclusion?

 

[VeeEight]

There is a vector that connects x with y, so the norm of this vector would be the distance between x and y.

 

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I am saying that just x is a pair of vectors in R^3. The cross product function takes that pair of vectors and gives you one vector (that is perpendicular to the original two).
So x is 2 vectors and y is another 2 vectors. What would |x-y| be?

Or is my understanding wrong? In that case, how can I approach the problem?