undergraduate vectors question

[low breach]

can someone please help me with this question?

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[low breach]

So the question basically asks you to find the point of intersection between L and the line that goes through Q and perpendicular to L

First, let's find the equation of the line L and the line, let's call it T, that goes through Q and goes perpendicular to L

Oh wait this is in space, it's harder now

Hmm

Oh I have an idea

I would find the equation of the plane that has normal vector v

And we just translate it with a scaled version of v until Q is in that plane

and that scalar shows how far the point R is compared to P in some sense

and with that we can find the exact position of R on the line L

[low breach]

I got this answer

Not sure if it's correct