Problem 1: (25 points) Given vectors A=i+2j+3k and B=2i+j-k in Cartesian form. (1) Determine the angle between the two vectors (in degrees), and (2) determine the orthogonal projection of A onto B, projB A. Problem 2: (25 points) Two forces F,and Fv are applied to a bracket, and their directions are shown in the figure below. Their resultant force R has a magnitude of 725 lb, and a direction shown in the figure. Determine the magnitudes of F,and Fv . Y .Problem 3: (25 points) The 20-kg homogeneous smooth sphere rests on the two inclined smooth surfaces as shown. Draw relevant free-body diagram(s), and determine the support forces on the sphere at A and B. Problem 4: (25 points) For the following set of linear equations: x+y+z=l x-y+z=2 x+y-z=3 (1) Write down the augmented matrix; (2) Find the reduced row-echelon form of the augmented matrix; (3)Find the solution from the reduced row-echelon form