Representing a plane equation using three points and three parameters l,m,n
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The question is
"Show that the set of points on the plane determined by the three points $(x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)$ is $[(frac{lx_1+mx_2+nx_3}{l+m+n},frac{ly_1+my_2+ny_3}{l+m+n},frac{lz_1+mz_2+nz_3}{l+m+n})]$ such that l+m+n$ne$0"
Just as a point on a line joining two points $(x_1,y_1,z_1),(x_2,y_2,z_2)$ can be represented as $(frac{kx_2+x_1}{1+k},frac{ky_2+y_1}{1+k},frac{kz_2+z_1}{1+k})$ s.t (k+1)$ne$0, where k is the parameter . The physical interpretation is that the line joining the two points are divided in the ratio 1:k.
This problem wants to extend this concept to the entire plane with l,m,n as the parameters.The solution must be simple but I am not able to solve it as I am new to analytical geometry
analytic-geometry
asked Dec 18 '18 at 4:21
Vinay VarahabhotlaVinay Varahabhotla
517
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add a comment |
$begingroup$
The question is
"Show that the set of points on the plane determined by the three points $(x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)$ is $[(frac{lx_1+mx_2+nx_3}{l+m+n},frac{ly_1+my_2+ny_3}{l+m+n},frac{lz_1+mz_2+nz_3}{l+m+n})]$ such that l+m+n$ne$0"
Just as a point on a line joining two points $(x_1,y_1,z_1),(x_2,y_2,z_2)$ can be represented as $(frac{kx_2+x_1}{1+k},frac{ky_2+y_1}{1+k},frac{kz_2+z_1}{1+k})$ s.t (k+1)$ne$0, where k is the parameter . The physical interpretation is that the line joining the two points are divided in the ratio 1:k.
This problem wants to extend this concept to the entire plane with l,m,n as the parameters.The solution must be simple but I am not able to solve it as I am new to analytical geometry
analytic-geometry
asked Dec 18 '18 at 4:21
Vinay VarahabhotlaVinay Varahabhotla
517
$endgroup$
1
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Barycentric coordinates.
$endgroup$
– amd
Dec 18 '18 at 5:11
$begingroup$
Yes found the answer thank you
$endgroup$
– Vinay Varahabhotla
Dec 19 '18 at 9:37
add a comment |
$begingroup$
The question is
"Show that the set of points on the plane determined by the three points $(x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)$ is $[(frac{lx_1+mx_2+nx_3}{l+m+n},frac{ly_1+my_2+ny_3}{l+m+n},frac{lz_1+mz_2+nz_3}{l+m+n})]$ such that l+m+n$ne$0"
Just as a point on a line joining two points $(x_1,y_1,z_1),(x_2,y_2,z_2)$ can be represented as $(frac{kx_2+x_1}{1+k},frac{ky_2+y_1}{1+k},frac{kz_2+z_1}{1+k})$ s.t (k+1)$ne$0, where k is the parameter . The physical interpretation is that the line joining the two points are divided in the ratio 1:k.
This problem wants to extend this concept to the entire plane with l,m,n as the parameters.The solution must be simple but I am not able to solve it as I am new to analytical geometry
analytic-geometry
asked Dec 18 '18 at 4:21
Vinay VarahabhotlaVinay Varahabhotla
517
$endgroup$
The question is
"Show that the set of points on the plane determined by the three points $(x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)$ is $[(frac{lx_1+mx_2+nx_3}{l+m+n},frac{ly_1+my_2+ny_3}{l+m+n},frac{lz_1+mz_2+nz_3}{l+m+n})]$ such that l+m+n$ne$0"
Just as a point on a line joining two points $(x_1,y_1,z_1),(x_2,y_2,z_2)$ can be represented as $(frac{kx_2+x_1}{1+k},frac{ky_2+y_1}{1+k},frac{kz_2+z_1}{1+k})$ s.t (k+1)$ne$0, where k is the parameter . The physical interpretation is that the line joining the two points are divided in the ratio 1:k.
This problem wants to extend this concept to the entire plane with l,m,n as the parameters.The solution must be simple but I am not able to solve it as I am new to analytical geometry
analytic-geometry
analytic-geometry
asked Dec 18 '18 at 4:21
Vinay VarahabhotlaVinay Varahabhotla
517
asked Dec 18 '18 at 4:21
Vinay VarahabhotlaVinay Varahabhotla
517
edited Dec 18 '18 at 5:07
Vinay Varahabhotla
asked Dec 18 '18 at 4:21
Vinay VarahabhotlaVinay Varahabhotla
517
asked Dec 18 '18 at 4:21
Vinay VarahabhotlaVinay Varahabhotla
517
asked Dec 18 '18 at 4:21
Vinay VarahabhotlaVinay Varahabhotla
517
517
1
$begingroup$
Barycentric coordinates.
$endgroup$
– amd
Dec 18 '18 at 5:11
$begingroup$
Yes found the answer thank you
$endgroup$
– Vinay Varahabhotla
Dec 19 '18 at 9:37
add a comment |
1
$begingroup$
Barycentric coordinates.
$endgroup$
– amd
Dec 18 '18 at 5:11
$begingroup$
Yes found the answer thank you
$endgroup$
– Vinay Varahabhotla
Dec 19 '18 at 9:37
1
1
$begingroup$
Barycentric coordinates.
$endgroup$
– amd
Dec 18 '18 at 5:11
$begingroup$
Barycentric coordinates.
$endgroup$
– amd
Dec 18 '18 at 5:11
$begingroup$
Yes found the answer thank you
$endgroup$
– Vinay Varahabhotla
Dec 19 '18 at 9:37
$begingroup$
Yes found the answer thank you
$endgroup$
– Vinay Varahabhotla
Dec 19 '18 at 9:37
add a comment |
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1
$begingroup$
Barycentric coordinates.
$endgroup$
– amd
Dec 18 '18 at 5:11
$begingroup$
Yes found the answer thank you
$endgroup$
– Vinay Varahabhotla
Dec 19 '18 at 9:37