The Foot of a Perpendicular from a Point to a Line












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I have a triangle $ABC$ and a point $P$ with barycentric coordinates $(alpha,beta,gamma)$ that I want to know the barycentric coordinates of the foot of a perpendicular from P to a line $l: ux + vy + wz = 0$






geometry barycentric-coordinates







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  • $begingroup$
    Any information of $u,v,w$?
    $endgroup$
    – El borito
    Jan 23 at 5:22










  • $begingroup$
    I'm looking for a general answer, but I'm interested L being the Euler line and P being B
    $endgroup$
    – Batman
    Jan 23 at 5:27
















1












$begingroup$


I have a triangle $ABC$ and a point $P$ with barycentric coordinates $(alpha,beta,gamma)$ that I want to know the barycentric coordinates of the foot of a perpendicular from P to a line $l: ux + vy + wz = 0$






geometry barycentric-coordinates







share|cite|improve this question











$endgroup$












  • $begingroup$
    Any information of $u,v,w$?
    $endgroup$
    – El borito
    Jan 23 at 5:22










  • $begingroup$
    I'm looking for a general answer, but I'm interested L being the Euler line and P being B
    $endgroup$
    – Batman
    Jan 23 at 5:27














1












1








1





$begingroup$


I have a triangle $ABC$ and a point $P$ with barycentric coordinates $(alpha,beta,gamma)$ that I want to know the barycentric coordinates of the foot of a perpendicular from P to a line $l: ux + vy + wz = 0$






geometry barycentric-coordinates







share|cite|improve this question











$endgroup$




I have a triangle $ABC$ and a point $P$ with barycentric coordinates $(alpha,beta,gamma)$ that I want to know the barycentric coordinates of the foot of a perpendicular from P to a line $l: ux + vy + wz = 0$






geometry barycentric-coordinates




geometry barycentric-coordinates






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 23 at 5:23









El borito

666216




666216










asked Jan 23 at 4:50









BatmanBatman

62




62












  • $begingroup$
    Any information of $u,v,w$?
    $endgroup$
    – El borito
    Jan 23 at 5:22










  • $begingroup$
    I'm looking for a general answer, but I'm interested L being the Euler line and P being B
    $endgroup$
    – Batman
    Jan 23 at 5:27


















  • $begingroup$
    Any information of $u,v,w$?
    $endgroup$
    – El borito
    Jan 23 at 5:22










  • $begingroup$
    I'm looking for a general answer, but I'm interested L being the Euler line and P being B
    $endgroup$
    – Batman
    Jan 23 at 5:27
















$begingroup$
Any information of $u,v,w$?
$endgroup$
– El borito
Jan 23 at 5:22




$begingroup$
Any information of $u,v,w$?
$endgroup$
– El borito
Jan 23 at 5:22












$begingroup$
I'm looking for a general answer, but I'm interested L being the Euler line and P being B
$endgroup$
– Batman
Jan 23 at 5:27




$begingroup$
I'm looking for a general answer, but I'm interested L being the Euler line and P being B
$endgroup$
– Batman
Jan 23 at 5:27










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