Let \(\mathbf{a} = (10, -6, 4)\) and \(\mathbf{b} = (7, 7, 3)\) be vectors.
(A) Find the scalar projection of \(\mathbf{b}\) onto \(\mathbf{a}\).
Scalar Projection:
(B) Decompose the vector \(\mathbf{b}\) into a component parallel to \(\mathbf{a}\) and a component orthogonal to \(\mathbf{a}\).
Parallel component:
Orthogonal Component: