Inner product doubt I have a doubt about a problem involving inner product spaces. The exercise is:
Given the subspace generated by the vectors $ (1,1,1) $ and $ (1,-1,0) $, find the orthogonal subspace and give a basis.
Now, what I understood of this problem is that I have to find the orthogonal complement. But they don´t give me any inner product to work with. Does the orthogonal complement vary with the product? Which one should I use?
I haven´t seen much of inner product, just the basic, but I should be able to solve this. Thank you! If you do not understand something, please ask me. 

The orthogonal component depends on the inner product. However, typically the inner product that is chosen (assuming you are dealing with a vector space over real numbers) is the following one:
$$\langle(x_1,x_2,x_3), (y_1,y_2,y_3) \rangle = x_1y_1 + x_2y_2 + x_3y_3$$
