For vectors p=⟨1,2,3⟩\mathbf{p} = \langle 1, 2, 3 \ranglep=⟨1,2,3⟩ and q=⟨−2,1,0⟩\mathbf{q} = \langle -2, 1, 0 \rangleq=⟨−2,1,0⟩, verify if they are orthogonal.
Yes, orthogonal since p⋅q=0\mathbf{p}\cdot\mathbf{q} = 0p⋅q=0
No, p⋅q=5\mathbf{p}\cdot\mathbf{q} = 5p⋅q=5
No, p⋅q=−3\mathbf{p}\cdot\mathbf{q} = -3p⋅q=−3
Yes, orthogonal since ∥p∥=∥q∥\|\mathbf{p}\| = \|\mathbf{q}\|∥p∥=∥q∥