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I want to write the equation of the line which passing the two point A(1, 1) and B(m+1, -2*m + 2) by using LinearAlgebra, but i can not write. Please help me. Thank you.

Hi,

Im trying to animate a simple pendulum with maple 15. I'm able to make to the pendulum masse move, but, somehow, I can't animate the rope of the pendulum. I tried to draw the rope with the plottools library line , but no success.

Pendulum:=proc(x,y)plots[pointplot]([x,y],color=blue, symbol=solidcircle,symbolsize=25) end proc:
A:=animate(Pendulum,[XCoordinate,YCoordinate],t=0..8,frame=100):
Rope:=plottools[line]([0,1],[XCoordinate,YCoordinate],color=blue,thickness=3):

Problem. write the equation of the line cut the two lines d1: x = 2*t, y= -t+1, z = t-2, d2: x = -1+2*m, y = 1+m, z = 3 and perpendicular to the plane 7*x+y-4*z=0. 

This is my code. 

> restart;with(geom3d):

with(LinearAlgebra):

a:=[2*t,-t+1,t-2]:

b:=[-1+2*m,1+m,3]:

line(d1,a,t):

line(d2,b,m):

With(geom3d), equation of  a line has the form a parametric equation. How  i can get canonical equation of a line? Please help me?

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));

Let A(1, 2, 3) be a point; d1: (x-2)/2 = (y+2)/(-1) = (z - 3) / 1

d2: (x--)/(-1) = (y - 1)/2 = (z  + 1) / 1.

Write the equation of the line passing through the point A, perpendicular to d1 and cut d2.

This is my code

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

A:=<1,2,3>:

B:=[2*t+2,-t-2,t+3]:

M:=<-m+1, 2*m+1,m-1>:

line(d1,B,t):

a:=convert(ParallelVector(d1),Vector):

v:=M-A:

Let (d1): x = 2*t +1, y = t-2, z =-2*t+2 and 

(d2): x = 2-m, y = 3+m,z = 4+m 

be two lines and (P): x - y + z - 6 = 0 be a plane. Write the equation of the line (Delta), knowing that (Delta) parallel to (P) and cuts (d1), (d2) at the points M and N, respectively so that MN = 3*sqrt(6).

Let A(1, -1, 3) is a point; (P): x + y + 5z = 0 be a plane; (l): x= 2t, y = -5t, z = 6t be a line. Write the equation of a line Delta parallel to the plane (P) and has a distance to (l) equal to 1.

I was thinking about this problem many times but i can not 

My problem: Write the equation of the line (Delta) passing the point A(-2;3;4), perpendicular to the line

(l): x = -t + 1, y = 2t, z = 3t + 1

and have a distance from the point B(1;2;-4) obtain

a) maximum;

b) minimum.

Can you write for me a code? Thank you.

Plase write for me a code for the following problem:

Let (d): (x-1)/2 = (y+2)/1 = z/1 be a line and

(P): x + 2y -z - 3 = 0 be a plane.

Write the equation of the line (Delta) lies in the plane (P), perpendicular to the line (d) and the distance between (d) and (Delta) equal to sqrt(2).

Problem. Write the equation of the line Delta which parallel to the planes 

(P): 3x +12y -3z -5 = 0, (Q): 3x -4y +9z + 7 = 0

and cuts two the lines

(d1): x = 2t -5, y = -4t + 3, z = 3t -1

(d2): x = -2m + 3,  y = 3m  - 1, z = 4m + 2.

This is my idea.

1) Put A(2t -5, -4t + 3, 3t -1) and B(-2m + 3, 3m  - 1, 4m + 2).

2) Find coordinates of vector AB.

3) Because Delta parallel to the planes (P...

Problem: Let (d): x = 2*t + 3, y = t -2, z = -t -1 be a line and (P): x+ y + z + 2 = 0 be a plane. Write the equation of a line Delta lies in the plane (P), Delta perpendicular to the line (d

Please write for me a proceduce in order to write the eqution of the common perpendicular to the two skewline 

d: x = 3*t - 7, y = -2*t +4, z = 3*t + 4 and

l: x = m + 1, y = 2m - 9, z = -m - 12.

I did:

with(geom3d);

line(d,[3*t-7,-2*t+4,3*t+4],t);

line(l,[m + 1,2*m - 9, - m - 12],m);

u:=ParallelVector(d);

v:=ParallelVector(l);

with(linalg);

w:=crossprod(u,v);

a:=crossprod(u,w);

have a list of lists, and I would like to write each of these lists on a separate file, *on a single line*.

For instance consider the following trivial example:

P := [[-.3819660120, .6180339880, -10000, -2], [.6180339880, 1.618033988, -10000, -1], [1.618033988, 10000, -10000, -.5], [2.618033988, 10000, -.5, -0.1e-3], [2.618033988, 10000, 0.1e-3, .5]]

I would like to create
 + a file named  P1.dat containing the line
     ...

How to solve this problem in maple?
Decide which of three lines given are tangent to the graph of f(x) at given points.
The function to define is f(x)=2x^3-4x^2+3x-5
The possible tangent lines are:
y = x - 5
y = 2x - 5
y = 3x - 5

1. What is/are the zero(es) for this function? In other words, what is the solution for f(x)= 0

2.  What axes values (x- and y- ranges) are appropriate for this graph?

3. When plotting each linear function with f(x...