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- Find a unit vector that is perpendicular to both A=4i-3j-2km and B=2i4j+3km.Determine the moment of the force F=9i+18jlb about point O by the following methods: (a) vector method using rF; (b) scalar method using rectangular components of F; and (c) scalar method using components of F that are parallel and perpendicular to the line OA.The magnitude of the force F is 55 lb. Calculate the moment of F about the x-axis using (a) the scalar method; and (b) the vector method.
- Find the internal force systems acting on sections 1 and 2.The force F=2i12j+5klb acts along the line AB. Recognizing that the moment of F about point B is zero, determine the x- and z-coordinates of point B.Determine the moment of the force F about point A in terms of F and d. Use (a) the scalar method; and (b) the vector method.
- Determine (a) the angle between the position vectors P and Q; and (b) a unit vector perpendicular to P and Q.It can be show that a plane area may he represented by a vector A=A, where A is the area and represents a unit vector normal to the piano: of the area. Show that the area vector of the parallelogram formed by the vectors a and b shown in the figure is A=ab.The force F of magnitude 200 N is perpendicular to the plane ABC. Determine the magnitude of its moment about the x-axis.
- Let A and B be two nonparallel vectors that lie in a common plane S. If C=A(AB), which of the following statements are true: (i) C = 0; (ii) Clies in plane S; and (iii) C is perpendicular to plane S?Find the moment about the origin due to the force F = -30i + 40k lb, which acts at the point (x,y,z) = (20,10,0) ft.Given that the moment along axis AC is150 lb.ft. Find the vector force, F.