Find parametric representation for the plane that passes through the point (1, 2, −3) and contains the vectors i + j − k and i − j + k.

Question

Find parametric representation for the plane that passes through the point (1, 2, −3) and contains the vectors i + j − k and i − j + k.

Answer 1

Normal vector of this plane n = det[(i j k) (1 1 - 1) (1 - 1 1) = i(1 - 1) - j(1 + 1) + k(-1 - 1) = - 2j - 2k.

So, equation of Plane: - 2(y - 2) - 2(z + 3) = 0; y + z + 1 = 0.

Parametric equation of this plane: r = <1, 2, - 3> + s<i1, 1, - 1> + t<1, - 1, 1>;

x = 1 + s + t; y = 2 + s - t; z = - 3 - s + t