Final answer:
The student's question likely involves finding an orthogonal vector rather than a vector reciprocal to a set of vectors in vector algebra, which can typically be obtained via the cross product operation using the cyclic order of unit vectors.
Step-by-step explanation:
The question pertains to vector algebra and involves finding a vector that is reciprocal to a given set of vectors. The original question appears to be asking how to find the reciprocal of a set of vectors (a, b, c). However, in vector algebra, the concept of a reciprocal vector is not common. Instead, problems often involve finding a vector that is orthogonal (perpendicular) to a given set of vectors, which can be achieved by using the cross product operation. If the goal is to find a vector reciprocally related to these vectors in magnitude and direction, it might mean taking the inverse of each vector's components, which does not have a standard definition in vector algebra.
In the case of finding a vector orthogonal to a given set of vectors, we usually look for the cross product of two of the vectors in the set since the cross product generates a vector orthogonal to both original vectors. Using the properties of cross products, we can find that the result of the cross product will be a vector that is orthogonal to the plane formed by the initial vectors. It's important to follow the cyclic order of unit vectors to determine the direction of the resulting vector based on the right-hand rule.
If the problem is to find a vector that is orthogonal to all three given vectors (a, b, c), this would usually imply finding the vector that is the result of the cross product of two of the vectors, and then the dot product of that result with the third vector should be zero.