Section$1\mathrm{.}3$: Problem $9$

$(1$ point$)$

Let $a=($:$-6,-1,-8$:$)$ and $b=($:$8,-1,3$:$)$ be vectors.

$($A$)$ Find the scalar projection of $b$ onto $a.$

Scalar Projection: $$

$($B$)$ Decompose the vector $b$ into a component parallel to a and a component orthogonal to $a.$

Parallel component: $$

$$

$$

Orthogonal Component: $$

$,)$