Question

A plane passes through the point (3, 4, 7) and is orthogonal to the vector < 8, −4, 1 >. Write the equation of the plane.

Answer 1

To write the equation of the plane, use a point on the plane and the normal vector of the plane. Substitute the values to get the equation in the form ax + by + cz = d.

Step-by-step explanation:

To write the equation of the plane, we need a point on the plane and the normal vector of the plane. The point given is (3, 4, 7), and the normal vector is < 8, -4, 1 >. The equation of the plane can be written in the form ax + by + cz = d. Substituting the values, we have 8(x-3) - 4(y-4) + 1(z-7) = 0. This simplifies to 8x - 4y + z = 20.