MaplePrimes - Questions and Posts tagged with coordinates

How to define a function?

toandhsp — Sat, 05 May 2012 08:08:43 Z

I have an equation of the plane Q: x + y + z - 1 = 0. Now i want to define a function

f:=(x,y,z)->lhs(Equation(Q)):

and i calculate the value f(1, 2, 3), but Maple understand. Plese help me.

If i want to substitute the coordinates N(a + 1, b + 2, c + 3) into the equation of the plane Q. What must i do?

How do i transform a vector field in cartesian coordinates to a vector field in polar coordinates?

Calon — Wed, 02 May 2012 15:10:06 Z

For example, i have the field x*e_x+y*e_y. Is there a command for transforming it into the same field with polar coordinates and polar unit vectors?

Coordinates of a point (10)

toandhsp — Thu, 15 Mar 2012 14:34:38 Z

Problem. In the plane 2*x -3*y +3*z -17 = 0, find a point M such that the sum of its distances from the poits A(3, -4, 7) and B(-5, -14, 17) will have the least value.

First way.

restart:with(geom3d):

point(A,3,-4,7):

point(B,-5,-14,17):

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

reflection(Q,A,P):

line(BQ,[B,Q]):

Coordinates of a point (7)

toandhsp — Wed, 07 Mar 2012 09:23:38 Z

Problem. Find the coordinates of the point M on the sphere (S): x^2 + y^2 + z^2-2*x+4*y+2*z-3=0 such that the distance from the point M

Coordiantes of a point

toandhsp — Fri, 10 Feb 2012 08:06:33 Z

Let M(1; -1; 0) be a point, Delta: (x-2)/2 =(y+1)/(-1) = (z - 1)/1 be a line, (P): x + y + z - 2 = 0 be a plane. Find the coordinates of the point A lies on (P), knowing that the line AM perpendicular to the line Delta and distance from the point A to the line Delta equal to sqrt(33/2).

This is my code

with(geom3d):

point(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:=ParallelVector(Delta):

Coordinates of a point (5)

toandhsp — Thu, 02 Feb 2012 09:29:08 Z

Let A(-5,-3,-3), B(0,1,-2) be two points and

(d): x = t - 3, y = 2*t, z = t+2.

Find the coordinates the point M on (d) so that the area of the triangle ABM obtain minimum value.

This is my code.

restart; with(LinearAlgebra):

A:=: B:=: M:=:

u:=A-B: v:=A-M:

T:=CrossProduct(u,v):

S:=minimize(1/2*Norm(T,2), location = 'true');

M:=subs(op(1,op(1, S[2])),M);

Coordinates of a point (4)

toandhsp — Thu, 02 Feb 2012 07:51:30 Z

Let A(-2, -1, 3), B(0, 1, 4) be two point and

(d): x = -t-2, y = t+1, z = -t-1 be a line.

Find coordinates point M lies on (d) so that area of the triangle ABM equal to 3*sqrt(5).

This is my code

restart; with(LinearAlgebra):

A:=: B:=: M:=:

u:=A-B: v:=A-M:

T:=CrossProduct(u,v):

sol:=solve(1/2*Norm(T,2)=3*sqrt(5),{t});

for i from 1 to 2 do print('M'[i]=(subs(op(sol[i]), M[1]), subs(op(sol[i]), M[2]),subs(op(sol[i]), M[3]))) end do;

Coordinates of a point (3)

toandhsp — Wed, 01 Feb 2012 09:16:40 Z

Let A(1,0,0) be a point and two lines

d1: (x-5)/3 = (y-1)/1 = (z - 2)/2,

d2: (x-5)/1 = (y-1)/1 = (z - 3)/3

Let B and C be two point lies on d1 and d2, respectively so that the three points A, B, C

coordinates of a point (2)

toandhsp — Sat, 28 Jan 2012 14:42:10 Z

Problem. Let A(-1,3,-2), B(-3,7,-18), C(2,-1,-3) be three points and (P):

2*x - y +z  + 1 = 0 be a plane. Find the coordinates of the point M lies on the plane (P) so that MA^2 + 2MB^2 + 3MC^2 obtain the minimum value.

This is my code.

restart: with(geom3d):
 A:=:  B:=:  C:=:
M:=: o:=:
eq:=solve([seq(o[i] = (A-M + 2*(B-M) + 3*(C-M))[i], i=1..3)]);
point(T, -1/6, 7/3, -43/6); # put T by my hand
plane(P,2*x - y +z  + 1 = 0,[x,y,z]):

Find coordinates of the point

toandhsp — Sat, 28 Jan 2012 08:54:56 Z

Problem. Let (P): 2x -y +2z + 9 = 0 be a plane and two points A(3,-1,2), B(1,-5,0). Find coordinates of the point M lies on (P) such that scalar product of two vectors MA and MB obtain the minimum value.

orthocenter of the triangle

toandhsp — Thu, 19 Jan 2012 07:45:50 Z

I wrote a program in order to find coordinates orthocenter of the triangle. Please comment for me. This is my code:

restart;

with(geom3d);

point(A,1,-3,0);

point(B,-2,1,1);

point(C,3,1,2);

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

line(BC,[B,C],t);

ab:=ParallelVector(AB);

bc:=ParallelVector(BC);

eq1:=Equation(plane(P,[C,ab],[x,y,z]));

eq2:=Equation(plane(Q,[A,bc],[x,y,z]));

eq3:=Equation(plane(ABC,[A,B,C],[x,y,z]));

How do i solve drawing a polar coordinates function?

englanderghost — Fri, 16 Dec 2011 17:28:50 Z

Hi guys

i have a problem to drawing this function

problem is F(r,theta)=sin(6r) /6r IF r is not 0

and F(r,theta)=1 IF r is 0

Thanks for your helps

how to change coordinate system for this equation ?

aryan_ams — Sun, 04 Dec 2011 21:07:36 Z

hi,

how to change coordinate system?

for example :

thx;

aryan.

Polarplot with error bars

11Quanta — Mon, 07 Nov 2011 15:53:22 Z

I've been trying to find a way to plot error bars in a polar coordinate system. Using ErrorPlot i can display my data with error bars in cartesian coordinates but the usual option 'coords=polar' doesn't seem to be followed. Perversely, the option 'axiscoordinates=polar' does work in ErrorPlot, so i just get a cartesian plot of my data sitting on top of a polar axis. Is there a way to plot my data with errors in a polar basis?

Plotting coordinates in maple

jpijnenburg — Thu, 15 Sep 2011 12:55:09 Z

This is the frame of the bike rear suspension i'm trying to calculate. Here is my maple sheet.

Download Maple-start.mw Maple-start.mw

What i'm trying to achieve is a plot that would look a little like this: