Length of a projection

MediumLinear Algebra~4m

Let $b=(4,3)$ and let $L$ be the line through the origin in the direction $a=(2,1)$ . Project $b$ orthogonally onto $L$ . What is the length of that projection vector? Give a decimal to four places.

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Projection length onto $a$ is $\dfrac{a\cdot b}{\|a\|}$ .
$a\cdot b=11$ , $\|a\|=\sqrt5$ .

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4.9193 (± 0.001)

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Length of a projection

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