A = ax + 4ay and B = 5ax – ay + 2az
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Given A = ax + 4ay and B = 5ax – ay + 2az
Determine the scalar projection of
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- Determine (a) the angle between the position vectors P and Q; and (b) a unit vector perpendicular to P and Q.Find a unit vector that is perpendicular to both A=4i-3j-2km and B=2i4j+3km.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?
- 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.For the position vectors P and Q shown, determine the orthogonal component of P Ă— Q in the direction of OA.A circular region of radius R/2 is cut out from the circular region of radius R as shown. For what distance d will kx for the new region be the same as kx (for the region before the cutout was removed?
- 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.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 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 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 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.