Final answer:
The dimension of a vector space spanned by vectors cannot be determined without specific vectors provided. For the part about orthogonal vectors, given vector A in the xy-plane, an example of vector B that is orthogonal to A with identical magnitude could be -4.0Î + 3.0ĵ.
Step-by-step explanation:
To answer the question about the dimension of a vector space spanned by vectors, we need to determine the number of vectors that form a basis for that space. If we are given a set of vectors, we must check if they are linearly independent, as linearly independent vectors span a vector space. However, the original question has not provided a specific set of vectors to assess, so we cannot give a definite answer without that information.
Regarding the second part of the question where vectors A and B are two orthogonal vectors in the xy-plane with identical magnitudes, and given that A = 3.0Î + 4.0ĵ, to find vector B, we would look for a vector also in the xy-plane that is orthogonal (at a right angle) to vector A. Since vector A has components (3, 4), we need to find vector B such that the dot product of A and B equals zero. One possible vector B could be -4.0Î + 3.0ĵ, as (3)(-4) + (4)(3) = 0. Remember that there are infinitely many vectors that could satisfy this condition if we account for different magnitudes and the negative counterpart, 4.0Î - 3.0ĵ.