Please help! How to use the vector z (the component of b orthogonal to ColA) to calculate the distance from b to ColA by using built-in function norm?

Theory: When the columns of A are linearly independent, a vector p is the orthogonal projection of a vector b∉ Col A onto the Col A if and only if p x = Aˆ , where xˆ is the unique least-squares solution of Ax b = , or equivalently, the unique solution of the normal equations T T AA A x b = . Also, if p is the orthogonal projection of a vector b onto Col A, then there exists a unique vector z, such that, z bp = − and z is orthogonal to Col A

[Walter Roberson]

How does this differ from https://www.mathworks.com/matlabcentral/answers/796882-please-help-how-to-express-p-as-the-projection-of-b-onto-the-col-a-according-to-the-theory-i-know?s_tid=srchtitle ?

[Tianlan Yang]

Hi, they are in the same exercise, but are two different questions. Do you need the entire instruction of it?