To solve the vector equation a\vec{A} + b\vec{B} + \vec{C} = 0, where \vec{A} = (75, -60), \vec{B} = (-16, 60), and \vec{C} = (84, 16), one must set up a system of equations based on the components of the vectors. The discussion emphasizes the need to create two equations from the x and y components to find the values of a and b. The magnitude of the resultant vector is noted to be zero, indicating that the vectors must balance each other out. Participants suggest using methods for solving simultaneous equations, though the original poster expresses uncertainty about how to proceed. Understanding the process of solving these equations is crucial for determining the values of a and b.
