Final answer:
Work done is calculated as the charge multiplied by the electric potential difference, which is integrated from the electric field along the charge's path. Without complete information about the electric field's position-dependent term, we cannot numerically integrate the work done.
Step-by-step explanation:
To calculate the work done in moving a 3 C charge along a straight line from point B (1,0,0) to point A (0,3,0) in an electric field E = 5 aₓ - 11.xaₒ V/m, we need to use the formula W = q∇V, where W is the work done, q is the charge, and ∇V is the electric potential difference experienced by the charge moving from B to A. The electric potential difference can be found by integrating the electric field along the path of the charge.
Since the electric field given includes a position-dependent term -11.xaₒ, we need to consider the component of the electric field along the path and its work on the charge. The exact integration might be complex depending on the full function represented by xaₒ. However, if the electric field were constant, the work done could be simplified as W = qEd, where d is the displacement along the direction of the field.
In the context of this question, to provide a numerical answer, further details about the function xaₒ are required to perform the integration to find the electric potential difference. If we had this information, we could integrate the component of the electric field along the path from B to A and then multiply by the charge (3 C) to find the work done in joules.