Answer
$\frac{14}{\sqrt {17}}$, $\lt\frac{14}{17}, \frac{56}{17}\gt$
Work Step by Step
Given: $a=\lt1,4\gt$ , $b=\lt2,3\gt$
Scalar Projection $b$ onto $a$ can be calculated as follows:
$\frac{a \times b }{|a|}=\frac{(1 \times 2)+( 4 \times 3)}{\sqrt {(1)^{2}+(4)^{2}}}$
$=\frac{2+12}{\sqrt {17}}$
$=\frac{14}{\sqrt {17}}$
Vector Projection $b$ onto $a$ can be calculated as follows:
$\frac{a \times b }{|a|^{2}}\times a=\frac{14}{17}\lt1,4\gt$
$=\lt\frac{14}{17}, \frac{56}{17}\gt$
Hence,
Scalar Projection $b$ onto $a$ = $\frac{14}{\sqrt {17}}$,
Vector Projection $b$ onto $a$=$\lt\frac{14}{17}, \frac{56}{17}\gt$
