Given a set of vectors, does every vector need to be "orthogonal" with the other for an orthogonal basis?

Question

If I take the set {(3, −2, 1, 3),(−1, 3, −3, 4),(3, 8, 7, 0)}, I immediately can tell that the set is orthogonal. If I were to extend this to R^4, and add a vector like (0,0,0,1), would the set still be an orthogonal basis for R^4? The new vector would be orthogonal to the third vector, but not the other two.

I appreciate the clarification.

Answer 1

All vectors need to be orthogonal between each other in an orthogonal basis.