MaplePrimes - answers and comments on Question, Equation of a line (6)

All right!

Kitonum — Mon, 06 Feb 2012 12:38:51 Z

I got the same answer. In my decision s and t are the parameter values for those points on the lines, for which is realized a distance equal to 1.

The code of my decision:

restart:

A:=<1, -1, 3>: u:=<a, b, c>: v:=<2, -5, 6>: M:=A+s*u: N:=t*v:

solve([a^2+b^2+c^2=1, DotProduct(<1, 1, 5>,u,conjugate = false)=0, DotProduct(M-N,u,conjugate = false)=0, DotProduct(M-N,v,conjugate = false)=0, Norm(M-N,2)=1],[a,b,c,s,t]);

a geometrical method.

toandhsp — Mon, 06 Feb 2012 20:04:07 Z

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

A:=<0,0,0>:

B:= <2,-5,6>:

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

P:=a*(x-A[1])+b*(y-A[2])+c*(z-A[3]):

Sol:=[solve({subs(x=B[1],y=B[2],z=B[3],P)=0,a^2+b^2+c^2=1,

abs(subs(x=M[1],y=M[2],z=M[3],P))=1},{a,b,c})]:

Equation(plane(alpha,subs(Sol[1], P)=0,[x,y,z])):

Equation(plane(beta,subs(Sol[2], P)=0,[x,y,z])):

n1:=convert(NormalVector(alpha), Vector):

n2:=convert(NormalVector(beta),Vector): plane(Q,x + y + 5*z = 0,[x,y,z]): n:=convert(NormalVector(Q),Vector):

s:= CrossProduct(n1,n): r:=CrossProduct(n2,n):

N:=<x,y,z>: [seq(N[i]=(M + s*t)[i],i=1..3)];

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

Another way

toandhsp — Tue, 07 Feb 2012 19:46:59 Z

restart; with(geom3d): with(linalg):

A:=<0,0,0>: # A on l

B:= <2,-5,6>: # B on l

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

P:=a*(x-A[1])+b*(y-A[2])+c*(z-A[3]):

Sol:=[solve({subs(x=B[1],y=B[2],z=B[3],P)=0,a^2+b^2+c^2=1,

abs(subs(x=M[1],y=M[2],z=M[3],P))=1},{a,b,c})]: # Equation of planes passing l and has a distance equal 1 from M

Equation(plane(alpha,subs(Sol[1], P)=0,[x,y,z])):

Equation(plane(beta,subs(Sol[2], P)=0,[x,y,z])):

n1:=NormalVector(alpha):

n2:=NormalVector(beta):

plane(Q,x + y + 5*z = 0,[x,y,z]): #Equation Q passing M and parallel to P

n:=NormalVector(Q):

s:= crossprod(n1,n):

r:=crossprod(n2,n):

convert(M,list):

point('M',op(%)):

Equation(line(Delta_1,[M,s],t));

Equation(line(Delta1_2,[M,r],t));

convert

toandhsp — Tue, 07 Feb 2012 13:07:10 Z

How can i convert M :=<1,-1,3> into point(M, 1, 2, 3)? Please help me. Thank you very much.

Answer

Kitonum — Tue, 07 Feb 2012 17:20:53 Z

convert(M,list); geom3d[point]('M',op(%));

[1, -1, 3]

Thank you.

toandhsp — Tue, 07 Feb 2012 17:25:47 Z

Thank you.