1. Let a force F be given by F = Fo(2i + 3j + 6k) where Fo is a constant. Determine the scalar component of F in the d = 8i + j + 4k direction. 2. The equation of a curve C is given by ( 4 + xy)? = ty-3. (a) Using implicit differentiation, find the slope of the curve at the point P(-1,4). (b) Determine y" at P. . P (c) Sketch the curve C in the neigh- bourhood of P. (Hint: Use the values of y' and y" obtained in parts (a) and (b) above.) O3. In my home office, I am trying to run a 12 metre long (blue) computer cable from the origin O on one wall to point S located on the opposite wall. It is hoped that point S will be as close as possible to my desktop computer, which is located at point Q(5, 2, 0) on the wall. Assume each wall is rectangular and all measurements are in metres. B N M S Q As shown in the diagram above, the (blue) cable will run directly to point M which is the midpoint of the points O and B(0, 4,3). It will then run horizontally from M to N and horizontally from N to P. From P the cable will run as far as possible along the straight line segment from P to Q. (a) Determine the coordinates of points M, N and P. (b) Determine the distance from point P to the point S where the cable stops. (c) Hence determine the coordinates of point S