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here is an application of dot products calculate the amount of work done when a sledge is pulled 50 meters by a force of 30 newton applied at an angle of 30 degrees with the ground now work done is force dot product of force and distance so work done w is force dot distance now we are given a force of 30 newtons so we write 30 newtons i mean let me write here 30 newtons dot distance is 50 meters and dot predator is f dot d is f d cos of theta the angle between the two vectors right times cos of 30 degrees right that is f dot d and you can use your calculator to find the answer so this is 50 times 30 times cos of 30 so you get 12.99.03 so approximately 1299 newton meter or you could write this as 1299 joules so that is the work done on the sledge when you pull it through a distance of 50 meters by a force of 30 newtons so this is a good application of dot product you should know that work done is scalar quantity right so itamp;#39;s just a number so that is how you should do it thank y