上浒文通大学 Vector manipulations SHANGHAI JIAO TONG UNIVERSITY Vector addition: A=Aeio B B=Bei08 C=A+B =B+A C=A+B=Aeio+Beioa B -(AcOS0+Bcose)+ (a) i(Asin0,+Bsing) A=C-B Vector substraction: B A=C-B=Ceioc-Beios B -(Ccosec -Bcoseg)+ (b) j(Csinec-Bsineg) Figure (a)Vector addition and(b)vector subtraction.Vector manipulations jθ Vector addition: θ A A j A e θ A = B j B e θ B = θ B =( cos cos )+ A B j j Ae Be A B θ θ θ θ =+= + + CAB =( cos cos )+ j( sin sin ) A B A B A B A B θ θ θ θ + + θ θ C C B j j Ce Be θ θ A CB =−= − Vector substraction: θ B =( cos cos )+ C B Ce Be C B θ θ =−= − − A CB j( sin sin ) C B θ C B − θ Figure (a) Vector addition and ( b) vector subtraction