Find the linear equation of the plane through the origin and perpendicular to the vector ⟨−5,4,4⟩.

Question

Find the linear equation of the plane through the origin and perpendicular to the vector ⟨−5,4,4⟩.

Answer 1

The standard form of the equation of a plane is:

            Ax + By + Cz + D = 0

             Where A, B, and C are from the vector Normal to the plane: N = [A, B, C]

With N and a point, (x0, y0, z0), the equation of the plane comes from simplifying:

             A(x – x0) + B (y – y0) + C( z – z0) = 0

Since your point is origin (0, 0, 0) and your Normal vector is [-5, 4, 4] the equation of your plane is:

             -5 (x – 0) + 4 (y – 0) + 4(z -0) = 0

             -5x + 4y + 4z = 0