Final answer:
The longer diagonal of a parallelogram with sides represented by the vectors 5a-2b and a-3b should be the vector 4a+b. However, none of the options given match this result, indicating an error in the question.
Step-by-step explanation:
The question pertains to finding the length of the longer diagonal of a parallelogram constructed with two given vectors.
In vector terms, this can be found by taking the difference between the two vectors that represent the sides of the parallelogram.
The given vectors are 5a-2b and a-3b. We attach the origin of the second vector to the origin of the first vector to form a parallelogram.
The longer diagonal is essentially the difference between the two vectors, hence, we calculate it as follows: (5a-2b) - (a-3b) which simplifies to 4a+b.
However, looking at the provided options, none of them correctly matches this result. Hence, there appears to be an error in the question or options provided.