Answer
$\frac{1}{\sqrt {21}}$,$\lt\frac{2}{21}, \frac{-1}{21},\frac{4}{21}\gt$
Work Step by Step
Given: $a=\lt2,-1,4\gt$ , $b=\lt0,1,\frac{1}{2}\gt$
Scalar Projection $b$ onto $a$ can be calculated as follows:
$\frac{a \times b }{|a|}=\frac{(2 \times 0)+( -1 \times 1)+(4 \times \frac{1}{2})}{\sqrt {{(2)^{2}+(-1)^{2}}+(4)^{2}}}$
$=\frac{0-1+2}{\sqrt {21}}$
$=\frac{1}{\sqrt {21}}$
Vector Projection $b$ onto $a$ can be calculated as follows:
$\frac{a \times b }{|a|^{2}}\times a=\frac{1}{21}\lt2,-1,4\gt$
$=\lt\frac{2}{21}, \frac{-1}{21},\frac{4}{21}\gt$
Hence,
Scalar Projection $b$ onto $a$ =$\frac{1}{\sqrt {21}}$,
Vector Projection $b$ onto $a$=$\lt\frac{2}{21}, \frac{-1}{21},\frac{4}{21}\gt$
