Answer
$4$, $\lt\frac{-20}{13}, \frac{48}{13}\gt$
Work Step by Step
Given: $a=\lt-5,12\gt$ , $b=\lt4,6\gt$
Scalar Projection $b$ onto $a$ can be calculated as follows:
$\frac{a \times b }{|a|}=\frac{(-5 \times 4)+( 12 \times 6)}{\sqrt {(5)^{2}+(12)^{2}}}$
$=\frac{-20+72}{13}$
$=\frac{52}{13}$
$=4$
Vector Projection $b$ onto $a$ can be calculated as follows:
$\frac{a \times b }{|a|^{2}}\times a=\frac{4}{13}\lt-5,12\gt$
$=\lt\frac{-20}{13}, \frac{48}{13}\gt$
Hence,
Scalar Projection $b$ onto $a$ = $4$,
Vector Projection $b$ onto $a$=$\lt\frac{-20}{13}, \frac{48}{13}\gt$
