Final answer:
To find the horizontal and vertical reactions at pin C, use the given vector components and apply the equation for the resultant force. This provides the total reaction at pin C. For first order reactions and equilibrium directions, graphing and free-body diagrams are typically used.
Step-by-step explanation:
In the context of engineering mechanics, finding the horizontal and vertical components of the reaction at a pin involves using vector analysis. The given components Cx = −2/3, Cy = −4/3, and C2 = 7/3 can be used to calculate the total reaction at pin C. The equation for the resultant force C is derived from the vector components by
C = √C²x + C²y + C²
Substituting the given values into the equation, we have:
C = √(−2/3)² + (−4/3)² + (7/3)² = √23/3
This calculation provides the magnitude of the reaction at pin C. To graph the components and check for first order reactions or the direction of equilibrium, you would usually create a free-body diagram to identify all forces acting on the system and then use trigonometry to find horizontal and vertical components if needed.