§22。 peration of the vectors 3. Vector difference by geometric methods The operation + ri is identical in all respects to the operation implied by C=A-B=A+(B N0eA-B≠B-AC≠A-B 4. The scalar(dot) product of two vectors The scalar product is a way to multiply two vectors to yield a scalar result Define: AB=ABcos A 82.2 operation of the vectors Notice OA, B are always positive ②6<T/2A.B= ARcos6>0 ③60>π/2A·B= ACos<0 ④6=π/2A·B= ACos6=0 ⑤A(B+C)=A·B+AC 5. The cross product of two vectors The new vector that results from the vector product has both a magnitude and a direction Define: C=AxB3 3. Vector difference by geometric methods The operation +(- ) is identical in all respects to the operation implied by - 1r r 1r r A r B r C A B A ( B) r r r r r = − = + − A r B r − C r 4. The scalar(dot) product of two vectors The scalar product is a way to multiply two vectors to yield a scalar result. Define: A⋅ B = ABcosθ r r §2.2 operation of the vectors Note: A− B ≠ B − A C ≠ A− B r r r r A r B r θ §2.2 operation of the vectors 5. The cross product of two vectors The new vector that results from the vector product has both a magnitude and a direction. Define: C A B r r r = × 1 A, B are always positive 2 θ < π/2 3 θ > π/2 4 θ = π/2 5 A⋅ B = ABcosθ > 0 r r A⋅ B = ABcosθ < 0 r r A⋅ B = ABcosθ = 0 r r A B C A B A C r r r r r s r ⋅( + ) = ⋅ + ⋅ Notice: