Question

Chapter 2, Problem 2/103 Express the 5.1-kN force F as a vector in terms of the unit vectors i, j, and k. Determine the scalar projections of F onto the x-axis and onto the line OA. 2 F-5.1 kNT 64° Answers: k) kN kN FOA kN

Answer 1

The component of force along z axis is given by 5.1sin33=2.778 kN

The component of force along x axis = 5.1cos33*cos64=1.875 kN

The component of force along y axis = 5.1cos33*sin64=3.844 kN

Therefore, the force in vector form = 1.875 i + 3.844 j + 2.778 k kN

scalar projection of force along a line is given by dot product of the force with the unit vector along the line

unit vector along x axis = i

dot product of force vector with unit vector along x axis =Fx= (1.875 i + 3.844 j + 2.778 k).(i) = 1.875 kN

unit vector along line OA=cos32 i + sin32 j = 0.848i + 0.530 j

dot product of force vector with unit vector along OA =F_OA= (1.875 i + 3.844 j + 2.778 k).(0.848i + 0.530 j) = 3.627 kN