Cartesian VectorMagnitudeDirectionsDot ProductCross ProductCartesian Position VectorCartesian Force VectorMoment of a ForceMoment of a Force About a Specified AxisSimplification of a Force and Couple System 1MR2O=M+MOFR=FuxuyuzrxryrzFxFyFzMa= u#r F=i j krxryrzFxFyFzMo=FdMo= r: F=F=Fu=Farrbr= 1x2-x12i + 1y2-y12j+ 1z2-z12ki j kAxAyAzBxByBzC= A B==AxBx+AyBy+AzBzA#B=AB cos ucos2 a+ cos2 b+ cos2 g= 1= cos ai + cos bj+ cos gkuA=AA=AxA i +AyA j+AzA kA= 2A2x+A2y+A2zA=Axi +Ayj+AzkEquilibriumParticleRigid Body-Two DimensionsRigid Body-Three DimensionsFrictionStatic (maximum)KineticCenter of GravityParticles or Discrete PartsBodyArea and Mass Moments of InertiaParallel-Axis TheoremRadius of GyrationVirtual WorkdU= 0k=BImk=BIAI=I+md2I=I+Ad2I=L r2 dm I=L r2 dAr= Lr'dWL dWr=r'WWFk=mkNFs=msNMx= 0, My= 0, Mz= 0Fx= 0, Fy= 0, Fz= 0Fx= 0, Fy= 0, MO= 0Fx= 0, Fy= 0, Fz= 0Fundamental Equations of Statics