Determine the equation of the plane passing through the points A(4,1,1) B(0,0,5) and C(2,7,2)

Answer 1

WE create vectors: BA = <4, 1, -4> and BC = <2, 7, -3>. Let normal vector to plane n = < k, l, m>.

Then, BA·n = 4k + l - 4m = 0;

BC·n = 2k + 7l - 3m = 0. If set l = - 4, we get system of equations: k - m = 1 and 2k - 3m = 28; k = m + 1;

2m + 2 - 3m = 28; m = - 26; k = - 25. So, vector n = < -25, - 4, - 26>.

Now equation of plane: - 25(x - 0) - 4(y - 0) - 26(z - 5) = 0; 25x + 4y + 26z - 130 = 0