Answer
Answer: 5.8
Work Step by Step
Dot product formula:
let vector a = $a"$
let vector b = $b"$
let dot product = .
$a . b $ $= abcos0$
$\frac{a" . b"}{b}= \frac{abcos0}{vector, b}$
$\frac{a" . b"}{b}= acos0$
$acos0$ is the component of vector a along the direction of vector b
$ acos0 = \frac{a" . b"}{b} $
$a".b" = (a"_i \times b"_i )+ (a'_j \times b"_j)$
$a".b" = (3\times 2) + (5\times 4)= 26 $
Finding the length of b:
$b= \sqrt (b^2_{x} + b^2_{y}) $
$= \sqrt (2.0^2+ 4.0^2) = 2\sqrt 5$
$acos0 = \frac{26}{2\sqrt 5} = 5.8$
