Find a vector parametric form and symmetric form, find minimal distance betwen L and P, consider vectors v and w.
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Alessandro Iraci
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By P w (v), you mean the projection of v on the line spanned by w?
Or the projection on the orthogonal space?
Yes the projection of v onto w.
Are you sure? This is a bit odd, as then the parallelogram would have area 0. The alternative makes more sense to me. Is there a definition you have on your notes or anywhere else?
I uploaded a file of some definitions I have, I'm not sure which one you would need.
Ok, that is indeed the projection onto w. This is odd, but it is what it is.
Do whichever you think is correct, I trust you. But also please keep your solution simple, I'm very much a beginner.
The area of the parallelogram determined by ⃗ v, ⃗ w ∈ R3 is ∥⃗ v × ⃗ w∥. I also found this definition.
Yes I know, but the text is asking for the area determined by Pw(v) and w. These two are parallel, so the area is 0.
I'll write both out in case there is an error in the text.
thank you so much, I really appreciate it.