Inner product spaces
General · Mathematics
Study notes
Q: In ℝ³ with dot product, find the angle between (1,1,0) and (1,0,1). Are they orthogonal to (0,0,1)? ⟨u,v⟩ = 1×1+1×0+0×1 = 1. ‖u‖ = √2, ‖v‖ = √2. cos θ = 1/2: θ = 60°! ⟨u,(0,0,1)⟩ = 0: ORTHOGONAL ✓! ⟨v,(0,0,1)⟩ = 1: not! (Angles via inner products!)