b. Express the force in Cartesian vector form. F = 1000 Ib 25° 130°
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- The three forces of magnitude P can be replaced by a single, equivalent force R acting at point A. Determine the distance x and the magnitude and direction of R.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 length of the position vector r is 240 mm. Determine the rectangular components of (a) r; and (b) the unit vector directed from O toward A.
- The three points A(0,2,2),B(1,4,1), and C(3,0,0) define a plane. The coordinates are in inches. Find a unit vector that is perpendicular to this plane.Find a unit vector that is perpendicular to both A=4i-3j-2km and B=2i4j+3km.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.
- 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.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.Determine the value of the scalar a if the following three vectors are to lie in the same plane: A=2i-j+2km,B=6i+3j+akm, and C=16i+46j+7km.
- The forces P1=110lb,P2=200lb, and P3=150lb are equivalent to a single force R. Determine (a) the magnitude of R; and (b) the coordinates of the point where the line of action of R crosses the yz-plane.Resolve A=3i+5j4k in. into two vector components-one parallel to and the other perpendicular to B=6i+2k in. Express each of your answers as a magnitude multiplied by a unit vector.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.