Given u=(1,1)u=(1, 1)u=(1,1) and v=(1,−1)v=(1, -1)v=(1,−1), are they orthogonal in the standard inner product space R2\mathbb{R}^2R2?
Yes, because u⋅v=0u \cdot v = 0u⋅v=0
No, because u⋅v≠0u \cdot v \neq 0u⋅v=0
Yes, because they are linearly independent
No, because they are linearly dependent