MaplePrimes - answers and comments on Question, Three points A, M, N lie on a straight line.

It is easy

Kitonum — Fri, 20 Jan 2012 23:34:27 Z

Try to write the code yourself!

Directions:

1) Find a plane passing through point A and plane d1

2) Find the point of intersection of the plane from 1) and plane d2

In some cases, your problem may have no solutions or have an infinite number of solutions.

toandhsp — Sat, 21 Jan 2012 21:21:59 Z

with(LinearAlgebra):

A:=<0,1,2>:  M:=<2*t,1 + t,-1 - t>: N:=<1+m, -1 -2*m,2+m>:

u:=A - M: v:=A-N:
w:=CrossProduct(u,v);

sys:=solve([t*m-(3+t)*(2+2*m) = 0, (3+t)*(-1-m) -2*t*m=0, 2*t*(2+2*m) +t*(-1-m)=0],[t,m]);

subs(sys[1],M);

subs(sys[1],N);

In this way, i don't know how to solve w = 0 in order to find m and t automatically. Please help me. Thank you very much.

Kitonum — Sat, 21 Jan 2012 23:04:48 Z

Your way is very good!

Here is the corrected code:

A:=<0,1,2>: M:=<2*t,1 + t,-1 - t>: N:=<1+m, -1 -2*m,2+m>:

u:=A - M: v:=A - N:

w:=LinearAlgebra[CrossProduct](u,v):

solve([seq(w[i]=0,i=1..3)]): assign(%):

'M'=M; 'N'=N;

toandhsp — Sun, 22 Jan 2012 04:22:18 Z

Thank you very much.