Another way

toandhsp — Fri, 10 Feb 2012 21:29:10 Z

restart;with(geom3d): with(LinearAlgebra):

M:= <1,-1,3>:

line(Delta,[2*t+2,-t-1,t+1],t):

plane(P,x+y+z+3 = 0,[x,y,z]):

a:=convert(ParallelVector(Delta),Vector):

n:=convert(NormalVector(P),Vector):

A:=<x,y,z>:

v:=DotProduct(A-M, a,conjugate = false):

B:=<2,-1,1>: # B lies on Delta

d:=Norm(CrossProduct(A-B, a), 2)/Norm(a,2):

sol:=solve([x+y+z+3 = 0, v = 0, d = sqrt(33/2)]);

coordinates(point('A1',op([seq(rhs(sol[1,i]),i=1..3)])));

coordinates(point('A2',op([seq(rhs(sol[2,i]),i=1..3)])));

Please comment to me. Thank you very much.

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