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 Post subject: distance from a point to a planePosted: Thu, 11 Sep 2008 02:25:44 UTC
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Joined: Mon, 29 Mar 2004 04:23:45 UTC
Posts: 27
Location: Charlotte
Let P be a point not on the plane that passes through the points Q,R, and S. Show that the distance d from P to the plane is
d = magnitude of (a * (b x c)) / magnitude of (a x b)
where a = QR, b = QS, and c = QP.

Use the distance to find the distance from the point (1,2,3) to the line x = 2 + t,
y = 2 - 3t, z = 5t

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 Post subject: Re: distance from a point to a planePosted: Thu, 11 Sep 2008 16:19:57 UTC
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Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 8306
Location: Lexington, MA

I have an "eyeball" approach to the formula . . .

Quote:
Let be a point not on the plane that passes through the points

Show that the distance from to the plane is: .
where: .

[Sorry, you'll have make your own sketch.]

The vectors determine a parallelepiped.

Its volume is: . .[1]

. . The volume is given by: .

. . The area of the base is given by: .

Substitute into [1]: .

Therefore: .

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