Vectors are

As far as a parallel vector to vector b went it would be just in the same direction and thus for expressing vector v as the sum of a vector parallel to vector b. I thought it would be

and for expressing the vector v as the sum of a vector orthogonal to vector b would be just

and so

However the answer given for the orthogonal part of the question is

I'm not sure what I have done wrong in the later part of the question.