Determine the magnitude and the direction angles abg of th

Determine the magnitude and the direction angles ( a,b,g ) of the resultant force F_r [ note : direction angle is the angel made by a vector with respect to one of the axes of a coordinate system, e.g. the Cartesian system. It is used to specify the direction of a vector ]

Solution

the vector notation of the force F_R = Fx i + Fy j + Fz k ,   where i , j , and k are the unit vectors along x y and z axis

                               Fx = F_R cos (a) , Fy = F_R cos(b) and Fz = F_R cos(g)

                                          F_R = F_R cos (a) i + F_R cos(b) j + F_R cos(g) k

                  magnitude of      F_R = sqrt (F_x² +F_y² + F_z²)

                                                     = sqrt (F_R²cos² (a)   + F_R²cos² (b)    + F_R²cos² (c) )

from the other diagrams we can see that F_R = F₁+ F₂

                                                                  magnitude of F_R = sqrt ( F₁²+F₂²)