8 2.3 the Cartesian representation of any vector Difference: A-B=(AI+A j+A, k)-B i+B j+B k) (A-B+(4-B)j+(4-B2)k Multiplication aA=a(Ai+Aj+A, k) =a4.i+a4,j+a4 Scalar product of two vectors: A B=(AI+A j+a, k). B i+Bj+B, k) AB+A, B,+Az 8 2.3 the Cartesian representation of any vector cross product of two vectors: AxB=(AI+A, j+A, k)(Bi+B,j+B, k) =(4,B-AB,)i+(4B-AB2)j +(AB1-1B)k i j k or AxB=A. A A B. BB Mnemonic Lijia7 §2.3 the Cartesian representation of any vector A B i A B j A B k A B A i A j A k B i B j B k x x y y z z x y z x y z ˆ ( ) ˆ ( ) ˆ ( ) ) ˆ ˆ ˆ ) ( ˆ ˆ ˆ ( = − + − + − − = + + − + + r r Difference: Multiplication: A i A j A k A A i A j A k x y z x y z ˆ ˆ ˆ ) ˆ ˆ ˆ ( α α α α α = + + = + + r Scalar product of two vectors: x x y y z z x y z x y z A B A B A B A B A i A j A k B i B j B k = + + ⋅ = + + ⋅ + + ) ˆ ˆ ˆ ) ( ˆ ˆ ˆ ( r r §2.3 the Cartesian representation of any vector cross product of two vectors: A B A B k A B A B i A B A B j A B A i A j A k B i B j B k x y y x y z z y z x x z x y z x y z ˆ ( ) ˆ ( ) ˆ ( ) ) ˆ ˆ ˆ ) ( ˆ ˆ ˆ ( + − = − + − × = + + × + + r r x y z x y z B B B A A A i j k A B ˆ ˆ ˆ × = r r or Mnemonic: i j k i j k ˆ ˆ ˆ ˆ ˆ ˆ + -