Answer
$\frac{8}{9}$, $\lt\frac{-8}{81}, \frac{32}{81},\frac{64}{81}\gt$
Work Step by Step
Given: $a=\lt-1,4,8\gt$ , $b=\lt12,1,2\gt$
Scalar Projection $b$ onto $a$ can be calculated as follows:
$\frac{a \times b }{|a|}=\frac{(-1 \times 12)+( 4 \times 1)+(8 \times 2)}{\sqrt {{(-1)^{2}+(4)^{2}}+(8)^{2}}}$
$=\frac{-12+4+16}{\sqrt {81}}$
$=\frac{8}{9}$
Vector Projection $b$ onto $a$ can be calculated as follows:
$\frac{a \times b }{|a|^{2}}\times a=\frac{8}{81}\lt-1,4,8\gt$
$=\lt\frac{-8}{81}, \frac{32}{81},\frac{64}{81}\gt$
Hence,
Scalar Projection $b$ onto $a$ = $\frac{8}{9}$,
Vector Projection $b$ onto $a$=$\lt\frac{-8}{81}, \frac{32}{81},\frac{64}{81}\gt$