1)Components of a vector A=A+A A=Ai+A i,j: represent unit vectors in direction of +X-axis or y-axIs 6 A= t80=A,/A
A A A i A j x y = ˆ + ˆ 2 2 A = A = Ax + Ay O x y Ay Ax tg = / i j ˆ ， ˆ :represent unit vectors in direction of +x-axis or +y-axis Ax Ay A Ax Ay = + 1) Components of a vector: A A i A A j x x y y ˆ , ˆ = =
2)Vector Addition A+B=? (1) adding with components, (2) adding by geometrical way. A=Ai+A1.B=B i+B C=A+B=(A+B3)+(A,+B,)j A+B B C=AtB P B P=P+p+
2) Vector Addition (1) adding with components; (2) adding by geometrical way. A+ B = ? B A C A B = + B A C A B = + P1 P2 P3 P4 ... P = P1 + P2 + P A A i A j B B i B j x y x y ˆ ˆ , = ˆ + ˆ = + j ˆ i ( A B ) ˆ C A B ( A B ) = + = x + x + y + y
3)Scalar Product(Dot Product) C=A·B= B·cos ARcos Suppose:A∥/B Then:A.B=A.BA·A=A B Suppose:A∥/-B Then: AB=-AB B EXample: W=F s: dw= F dr
3) Scalar Product (Dot Product) ABcos C A B A B cos = = = B A A B Suppose: // AB = AB Then: 2 A A = A A B Suppose: //− AB = −AB Then: B A A B Example: W F S dW F dr = ; =
4)Vector Product (Cross Product C= AxB C=AXB C=lAx B= AB sine B日 Direction: determined by right-hand rule Suppose:A∥BorA∥-B Then:AxB=0A×A=0 Example:M=F×F;L=F×mv
4) Vector Product (Cross Product) C = A B = ABsin C A B = B A C A B = A Bor A B Suppose: // //− A B = 0 Then: A A = 0 Example: M r F L r mv = ; = Direction: determined by right-hand rule c
2. Physics quantities to describe the particle motion 2.1 Position Vector, Displacement and Motional Equation 1)position vectors r=OP=0A+ AB+ Bp aP(x,y, r=xi+ vi+zk Magnitude is determined by: r+ytz Direction is determined by: x cosa=x/r; cos B=y/r; cosy=z/r cos a+coS B+cos y=1
2. Physics quantities to describe the particle motion 2.1 Position Vector , Displacement and Motional Equation 1) position vectors r xi yj zk ˆ ˆ ˆ = + + cos cos cos 1 cos / ;cos / ;cos / 2 2 2 + + = = = = x r y r z r Direction is determined by: 2 2 2 r = r = x + y + z Magnitude is determined by: → r = OP → → → = OA+ AB+ BP o x y z •P(x,y,z) x y z A B C r