Linear Algebra: Distance From a Point and a Line in R^3

kyle1

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Aug 24, 2017
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Question: Find the distance from the point B = (1, 1, 1) and the line l through the point A = (-1, 1, 2) and the direction vector d = [1, 0, 1].

Here is what I've found:
Vector Form of line l (maybe?):
[-1, 1, 2] + t[1, 0, 1] = [-1+t, 1, 2+t] = I call it the vector x
And the parametric equations:
x = -1 + t
y = 1
z = 2 + t

I think what I need to do is find the projection of vector b onto vector x which would be:
x • b ________________ ____x • b
------- * x or it's also equal to --------- * x
x • x ___________________ _|x|^2
So if all of my thinking is correct, my only problem is I don't know how to do a project in R^3. Especially not with a vector in parametric form which is all I can seem to get it in. Is there any advice, or a reference you can point me towards - I haven't been able to find any so far ...
 
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