"In practice problem 5 question 9 a and b. Why a and b need to use different method?"

The projection formula requires an orthonormal basis.

--- 9a

The basis is already orthogonal so we just need to normalise the vectors (make the unit length) and then we have an orthonormal basis.

--- 9b

The basis is not orthogonal so we need to construct one using the Gram-Schmidt process.

The first part of the Gram-Schmidt process produces an orthogonal basis {w_1 w_2,...}. At this point we are in the same position as question 9a.

The last part of Gram-Schmidt is to normalise the vectors to make the basis orthonormal. This is what we did in question 9a.