The following code computes the total work done against gravity by the $2$ tensions and the weight of the piano in problem $9$ above. $$np$.$dot$$ is a function that computes the algebraic definition of the dot product. Manually, that is$,$ using pen and paper, evaluate the code by substituting the numbers in the appropriate places. For example, the first time you run the loop, $$magnitude$$ will be $1830$ and $$angle$$ will be $120$ since the first tuple of the $$forces$$ list is $(1830,120).$ In the next line of code, $$force$\_$x$$ will be $1830$cos$(120)=-915,$ and so on$.$ a$.$ What is the total work done against gravity? Why do you think this is the case? b$.$ How does the code solution compare to your other solution for problem $9?$ c$.$ What changes would you make to the code if you wanted to compute only the work done by weight against gravity?