Problem 1: Given a four-bar mechanism in which the position vectors \(R_1 = 6i\) inches and \(R_2 = 3i + 2j\) inches are given. In addition, it is known that link 3 is horizontal and link 4 is vertical at this particular instant.
Required:
a. (10) Graphically determine the position vectors \(R_3\) and \(R_4\) (magnitude and direction)
b. (25) Analytically determine the position vectors \(R_3\) and \(R_4\) (magnitude and direction) using the loop closure equation. Present your solutions in complex algebra notation (i.e., i, j, and k vector components).