Final answer:
To find the x, y, and z components of the reaction at the joint, apply trigonometric functions to resolve the given vectors into components along the axes. Sum these components as per static equilibrium to solve for the unknowns.
Step-by-step explanation:
To determine the x, y, and z components of the reaction at the ball-and-socket joint A, we need to use the given data and apply the principles of statics and vector resolution. The vector components along the axes can be found using the trigonometric relationships.
For the x-components, we use the equation Ax = A cos 0. Given that A = 53.0 m and 0 = 20.0°, we can calculate Ax. Similarly, the y-components can be calculated using Ay = A sin 0. Once these components are found for both vector A and vector B (with given B = 34.0 m and g = 63.0°), they can be summed accordingly to find the resultant components in the x and y directions.
Finally, the equilibrium conditions must be applied to the object in question to solve for any unknowns. This involves setting the sum of all component forces in each axis direction to zero, as no motion means the net force is zero (static equilibrium). In this case, you will sum the momenta in both x and y directions. With this information and the equilibrium equations, you can solve for the x, y, and z components at the ball-and-socket joint.