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Question: Equation of a line (9)

Question:Equation of a line (9)

toandhsp 300
geom3d line
February 11 2012
0

Write the equation of the line passing through the point A(2, 2, -5), parallel to the plane (P): 2x +3y -z - 17 = 0 and cut the line Delta: x = -2 +3*t, y = 4-t, z = 5 + 2*t.

1) First code.

restart:

with(geom3d):

point(A,2,2,-5):

line(Delta,[-2+3*t,4-t,5+2*t],t):

plane(P,2*x+3*y-z-17=0,[x,y,z]):

parallel(Q,A,P):

Equation(Q):

coordinates(intersection(B,Delta,Q)):

Equation(line(AB,[A,B],t));

 

2) Second code

> restart: with(LinearAlgebra): with(geom3d):

A:=<2,2,-5>:

M:=<-2+3*m,4 - m,5+2*m>:

plane(P,2*x + 3*y - z - 17 = 0,[x,y,z]):

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

v:=M-A:

solve(DotProduct(v,a,conjugate=false)=0,{m}): assign(%):

'M'=M: N:=<x,y,z>:

[seq(N[i]=(A + (M-A)*t)[i],i=1..3)];

 

Please comment to me. Thank you very much.
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