Answer
$\frac{9}{7}$,$\lt\frac{27}{49}, \frac{54}{49},\frac{-18}{49}\gt$
Work Step by Step
Given: $a=\lt3,6,-2\gt$ , $b=\lt1,2,3\gt$
Scalar Projection $b$ onto $a$ can be calculated as follows:
$\frac{a \times b }{|a|}=\frac{(3 \times 1)+( 6 \times 2)+(-2 \times 3)}{\sqrt {{(3)^{2}+(6)^{2}}+(-2)^{2}}}$
$=\frac{3+12-6}{\sqrt {49}}$
$=\frac{9}{7}$
Vector Projection $b$ onto $a$ can be calculated as follows:
$\frac{a \times b }{|a|^{2}}\times a=\frac{9}{49}\lt3,6,-2\gt$
$=\lt\frac{27}{49}, \frac{54}{49},\frac{-18}{49}\gt$
Hence,
Scalar Projection $b$ onto $a$ = $\frac{9}{7}$,
Vector Projection $b$ onto $a$=$\lt\frac{27}{49}, \frac{54}{49},\frac{-18}{49}\gt$
