Does |xy| ≤ |x| + |y| hold for vectors?

[Bertrandkis]

Homework Statement

Let x and y be to vectors
Verify whether |xy|<=|x|+|y| for all x,y

The Attempt at a Solution

My first problem with this question is that it does not tell us whether the operation xy is the same as x.y (dot product) or a cross product.

 

[HallsofIvy]

Your are right. That is a problem. I am also surprised that is not $|x|^2+ |y|^2$ on the right. I suspect that they mean dot product. I suggest you look at $|(x-y)\cdot(x-y)|$.