8 2.3 the Cartesian representation of any vector 3. The case of three dimensions A=Ai+Aj+Ak n prove that A=(4.4)2=(42+42+4 Ai=Acos%= A Ak A·j= Acos B Ak=AcOS y=A s 2.3 the Cartesian representation of any vector cos a+ cos B+cos y=1 4. The operations of vectors in Cartesian coordination system Addition: A+B=(Ai+A j+A, k)+(Bi+B j+B,k) (4+B3)+(A,+B)j+(42+B)k6 §2.3 the Cartesian representation of any vector 3. The case of three dimensions A r A i x ˆ Azk ˆ A j y ˆ x y z A A i A j A k x y z ˆ ˆ ˆ = + + r z y x A k A A A j A A A i A A ⋅ = = ⋅ = = ⋅ = = γ β α cos ˆ cos ˆ cos ˆ r r r We can prove that 1 2 2 2 2 1 2 ( ) ( ) A A A = Ax + Ay + Az = ⋅ r r §2.3 the Cartesian representation of any vector 4. The operations of vectors in Cartesian coordination system Addition: 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 x x y z x y z ˆ ( ) ˆ ( ) ˆ ( ) ) ˆ ˆ ˆ ) ( ˆ ˆ ˆ ( = + + + + + + = + + + + + r r cos cos cos 1 2 2 2 α + β + γ = x y z γ β α A r