The vertices of a triangle are (x1,y1,z1) , (x2,y2,z2) and (x3,y3,z3). Explain how to find a vector perpendicular to the triangle. I said : A vector perpendicular to the triangle can be found by multiplying a point on the triangle by the vector. If the result is 0, then the vector is perpendicular to the triangle. Is this right?
-
What do you mean by "multiply a point on the triangle by a vector"? You seem to be thinking about the dot product, but knowing that the dot product of orthogonal vectors is zero doesn't indicate how to FIND a vector that is perpendicular.
Assuming that the three points actually define a triangle, they also define a plane---the plane that contains that triangle. To find the directions in IR^3 that are perpendicular to the triangle, use a cross product.
If P = (x1, y1, z1), Q = (x2, y2, z2) and R = (x3, y3, z3), form the vectors u = PQ and v = PR. A vector perpendicular to the triangle is u x v (that should be read "u cross v").
Assuming that the three points actually define a triangle, they also define a plane---the plane that contains that triangle. To find the directions in IR^3 that are perpendicular to the triangle, use a cross product.
If P = (x1, y1, z1), Q = (x2, y2, z2) and R = (x3, y3, z3), form the vectors u = PQ and v = PR. A vector perpendicular to the triangle is u x v (that should be read "u cross v").