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Question: Equation of a plane (6)

Question:Equation of a plane (6)

toandhsp 300
geom3d
January 30 2012
0

Problem. Write the equation of the plane passing the point H(2, 1, 1) and cuts the coordinates Ox, oy, oz at A, B, C respectively so that H is orthocenter of the triangle.

This is my code.

restart:

with(geom3d):

with(LinearAlgebra):

A:= <a,0,0>:

B:=<0,b,0>:

C:=<0,0,c>:

H:=<2,1,1>:

f:=(x,y,z)->x/a + y/b +z/c-1:

eq:=solve([f(H[1],H[2],H[3]) = 0,DotProduct(B-C, A-H, conjugate = false) = 0,DotProduct(A-C, B-H, conjugate = false) = 0],{a,b,c}): assign(%):

sort(Equation(plane(P,x/'a' + y/'b' +z/'c'  - 1 = 0,[x,y,z])));

Please comment to me. Thank you very much.
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