Orthogonal bases for the eigenspaces.

Question

I'm looking at a math problem which I have the solution for. The question looks like this:

Question

By hand, calculate the eigenvectors and find orthogonal bases for the eigenspaces.

The eigenvalues are eigenvalues

Solution

Image of the solution

My problem

In the solution it is written "It is easily checked that v3 is orthogonal to v1 and q2"

When vectors are orthogonal to each other the inner product should be equal to zero. But and is not equal to zero as far as I can see. What am I missing? Is the solution wrong? (I guess not).

Best Regards Christian