Thread: Question on 3-d vectors

A triangle has vertices at the points A(5,0,0), B(0,5,0), and C(0,0,5). Identify the point in the interior of the triangle that is closest to the origin.

Originally Posted by dalbir4444

A triangle has vertices at the points A(5,0,0), B(0,5,0), and C(0,0,5). Identify the point in the interior of the triangle that is closest to the origin.

1. The points A, B, C define a plane:

x,y,z)=(5,0,0)+r(5,-5,0+s(5,0,-5)" alt="px,y,z)=(5,0,0)+r(5,-5,0+s(5,0,-5)" />

2. p in normal form:

Thus



3. The point F lies on the line through the origin perpendicular to p:



4. Calculate the point of intersection:



Therefore