Vectors in 3d Bracket Notation: V= [Vz, VY] 1 SimV COST Decomposing Using Components v=aA + bB+ c? V = a Ax Ay A2 + 6 82 Cx + Cy Cz V2 = aAz + 6Bx + CCx Vy =Q Ay + b By + c Cy V2 = QAz + bB2 + CC2 Ax Bx Cx Ay By Cy Az B2 C2 Vx Vy V2 Matrix Multiplication Ax Bx Cx Ay By Ly 1 Az B2 C2 Vx - Vy = LV2 Maginude of 2D vector: V= VVx2+ vy2 Maginade of 30 Vector: V=V2 + v+ + v2 If we divide the vector by its own mag. We get a Unit vector v= Y V2 + V2 + V2 V - Unit vector describes the direction v - Unit Vector is 1 and dimensionless Unit Vector Notation: = +x direction j=ty direction R = +2 direction V=îVx+îVy+ÊVz
Reading 3d Diagrams Diagrams m. - x, Y, 2 are 90° to each other uther the x axis. 0.0 and A Az= ACOSO Ax= Asino COSA Ay = Asingsino Cartesian Vectors 2 r a RB ! V2 1 Unit Vector: 1 Sin Cos 07 Sind sino cose Cosa = V Cos B = Vy cos Y = Vz Y V - - F1= 0; + 350 Sin 40j + 350 cos 40K F2= 100 LOS451+100 COS 60j-100 LOS 1200K Fg=250 COS60°- 250 COS45j + 250 COS 60 K con vector form and determine the magnitude and coordinate the resultant force. clown, Expr F 3= 250 N z Fiz F .= 350N Fax -40° 60° 45 60 45 Fi= 224.971+ 268H&K F2: 70.7107;+ 505-805 F3=125-176.77 +ask 1209 - FR= F1+ F2+ F3 FR = 195.7i + 98.195+393.12K 60 F2= 100 N FR= (195.7)2+(98.19)2+(343.12) FR= 407.035 N 98.19 407.035 407.035. B=COS" r=Cos-"( 343.12 407.03