P2 has a mysterious inner product * for which {x+4, 3x-5} is an orthonormal basis. IS there enough information to tell what is the length of 1? If so, compute it. If not say why not.
To determine if there is enough information to find the length of the vector 1, we need to consider the properties of the inner product * and the orthonormal basis {x+4, 3x-5}.
In an orthonormal basis, all the vectors are mutually perpendicular and have a length of 1. Since {x+4, 3x-5} is an orthonormal basis, the length of each vector in this basis is 1.
Therefore, if the vector 1 is a linear combination of the vectors in the given orthonormal basis, its length can be determined. To find the length of 1, we need to express it as a linear combination of the basis vectors and calculate its length.
However, the vector 1 is not given in the question, so we do not have enough information to determine its length. We would need the specific coordinates or representation of the vector 1 in order to find its length.