Mathematics Proof - Advanced Math

[Ultima Designs]

This is essentially for a Calc II class, can anyone help? You'd be my hero, and I'll give you a kiss or something:

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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 = absolute value( (a X b) . c )
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absolute value( a X b )

where a = vector QR, b = vector QS, and c = vector QP.

("." signifies dot product, "X" signifies cross product)

[Frets]

http://board.flashkit.com/board/forumdisplay.php?f=63

[Ultima Designs]

Thought that was for Flash math and the like...this is for my Multivariate Analysis and Approximation class. I don't think this is the first math problem posted in the CL...

[yasunobu13]

I'll give you a hint
1) a X b gives the normal of the plane.

2) vector c is a vector from the plane to a point in space.

3) Taking the dot product of one vector to another is the same as projecting one vector to another and finding the projected distance.

4) the distance from a point to a plane is the distance from that point to the plane along the plane's normal.


another interesting note, d will equal the volume of the parallelepiped formed by a, b and c