April 20, 2014

Homework Help: Linear Algebra

Posted by Nikki on Sunday, March 1, 2009 at 12:52am.

In 3-space, a plane abc is spanned by three points a, b, c. The point x does not lie on this plane.

I'm trying to find the formulas used to find the point p on abc with minimal distance to x.

I know the point p must be perpendicular to the point p and the plane.

So, I began with taking a vector from the plane to the point, w:

x = (x0,x1,x2)
p = (p0,p1,p2) <-- unknown

w = [p0-x0, p1-x1, p2-x2]

v = [a, b, c] = [a0 b0, c0]
[a1, b1, c1]
[a2, b2, c2]

then I project w onto v

D = |(v dot w)|/|v|

but my problem arises here because I do not know the distance and I do not know the coordinates of p. Am I supposed to be using the gradient formula instead?

Any help is greatly appreciated! Thank you

Answer this Question

First Name:
School Subject:

Related Questions

Geometry - 4.Determine which point does not lie on the graph of the line y=x-3 a...
maths - geometry - In a space with an orthonormal coordinate system consider the...
Geometry Honors - You and your friend each draw 3 points. Your points lie in ...
Algebra - Let A(4,3) B(5,8) and C(3,10) be three points in a coordinate plane. ...
Precalc - At the point were a line intersects a plane [with the equation (24x+...
math - Given the plane 2x-3y+7z=4, a) Find the equation for the line ...
Math - Okay heres the pic. There is a plane with points B,D, and E.those [oints...
Geo Hons - Okay heres the pic. There is a plane with points B,D, and E.those [...
Geometry - I need help with these problems: 11. The 2 captains of the school ...
Calc - "Consider the surface given by 4x^2-y^2+5z^2-10z=55. a) Find all points ...