Problem: Let (d): x = 2*t + 3, y = t -2, z = -t -1 be a line and (P): x+ y + z + 2 = 0 be a plane. Write the equation of a line Delta lies in the plane (P), Delta perpendicular to the line (d) and the distance from point M (1,-3, 0) to Delta equal to sqrt (42).
This is my idea
Let H(x,y,z) be projection of the point M on the line Delta. We find a, b, c from the following conditions:
1) H lies on (P);
2) Vector(MH) perpendicular to direction vector a = (2, 1, -1) of (d);
3) MH = sqrt(42).
and my code
From here, I do not know how to call H is projection of M on Delta. Please help me. Thank you very much.