Finding orthogonal of two vectors

[omer10000]

Homework Statement

A vector in lR 3 (basis) has vector space V with the standard inner product.

I need to find a vector in V which is perpendicular to both vectors
v_1 = (1,2,1)^T and v_1 = (2,1,0)^T

Homework Equations

There is no real important equations other than just using matrix and linear transformation principles.

The Attempt at a Solution

My attempt has gone nowhere. I used dot product to show the two vectors are not perpendicular and that's about it. It's probably real simple but I just don't get it.

 

[fzero]

Do you know about the cross product of vectors? If you don't, can you write down the conditions that an arbitrary vector $\mathbf{w} = (w_1,w_2,w_3)$ must satisfy to be orthogonal to those vectors?