Let ${\mathbf a} = (-6, 2, -7)$ and ${\mathbf b} = (6, 10, 1)$ 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: (, , )