derivation of the formula circled

[spiral geyser]

what is the derivation of the formula circled?

[bronze panther]

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[river veldt]

Well

$$d=p \cdot n$$

[young star]

PapaBread

[river veldt]

And to project with dot product you need to divide by the norm of the vector youre trying to project onto

$$proj_n p = \frac{p \cdot n}{\abs{n}}$$

[young star]

PapaBread

[river veldt]

So if you just substitute d into this and expand norm(n) then you get your formula

$$proj_n p = \frac{d}{\sqrt{n_1^2+n_2^2+n_3^2}}$$

[young star]

PapaBread

[river veldt]

@spiral geyser

Heres a visualization of what we're doing if it helps at all

You can see how the projection onto n of p gives you the distance to the origin

[spiral geyser]

sorry for the extremely late response and thank you

[hearty sonnet]

@spiral geyser has given 1 rep to @river veldt

[river veldt]

Thats no problem Im glad to have helped

If you need any more explanation just ask

[spiral geyser]

i will man thank you 🙏