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- 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?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.For the position vectors P and Q shown, determine the orthogonal component of P Ă— Q in the direction of OA.
- Find a unit vector that is perpendicular to both A=4i-3j-2km and B=2i4j+3km.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.Determine (a) the angle between the position vectors P and Q; and (b) a unit vector perpendicular to P and Q.
- The combined moment of the two forces, each of magnitude P, about point A is zero. Determine the distance d that locates A.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.The chain OA is 25 ft long and weighs 5 lb/ft. Find the maximum force in the chain and the distance H.
- The moment of the force F=50i100j70klb about point O is MO=400i+410j300klbft. Determine the coordinates of the point where the line of action of F intersects the xz-plane.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.A force F = 7.45 kN directs from point E (0, 3, 6) to point A (0, 0, 8) and rotates about the DK-axis, where point D (2.5, 6, 4) and point K (2.5, 0, 0). All distances are in meters. Determine the moment produced in kNm.