Find two vectors in r2 with euclidian norm 1
whoseeuclidian inner product with (3,1) is zero.

Step-by-step explanation:

First we define two generic vectors in our space:

By definition we know that Euclidean norm on an 2-dimensional Euclidean space is:

Also we know that the inner product in space is defined as:

So as first condition we have that both two vectors have Euclidian Norm 1, that is:

and

As second condition we have that:

Which is the same:

Replacing the second condition on the first condition we have:

Since we have two posible solutions, or . If we choose , we can choose next the other solution for .

Remembering,

The two vectors we are looking for are: