Final answer:
The student appears to have mixed various concepts including matrix commutation, vectors, and quadratic equations, which needs clarification to provide a specific answer.
Step-by-step explanation:
The student is asked to find values for constants a, b, c, and d for which matrices A and B commute. Commutative property in matrix algebra implies that two matrices A and B commute if AB = BA. However, the question provided seems to be a mix of different mathematical problems where vectors, dot products, and cross products are mentioned, but this context is not enough to determine how a, b, c, and d relate to matrices A and B commuting.
For dot products and cross products of vectors, it's essential to use the established algebra of vectors, which includes the distributive and anticommutative laws for cross products and the commutative law for dot products.
Given the information, the student could be asked about the properties of vectors operations or the quadratic formula where constants a, b, and c are given, but this does not directly relate to matrices commuting.