A constant force F = 24i + 35j moves an object from the point P=(5,4) to the point Q=(2,10), where units are in pounds and feet. Find the work done. F,i, and j are vectors. Given answer is 260 ft-lb

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JDavid -I get an answer of 138 ft-lb and pretty confident that is the correct answer.First, move the vector PQ to start at the origin by creating the component vector <-3,6>Work Done is defined as W = F*d or Force times distance.The distance d is pretty simple to calculate.  It is the length of the component vector <-3,6>, which I'll call vector c. The length of vector c is the distance d that the object moves:d= The Force (F) is a little more difficult to calculate.  It is the projection of F onto the component vector c.  The formula for this is:proj cF = (c dot F) ÷ ||c||where ||c|| is the length of vector c = So, proj cF = [(-3i + 6j) dot (24i + 35j)]/proj cF = 138/Work Done = Fd = 138/* = 138 ft-lbHope that helps