Final answer:
To find the equation of the plane passing through a given point and perpendicular to a line, use the formula for the equation of a plane.
Step-by-step explanation:
To find an equation of the plane that passes through the point (6, 4, 4) and is perpendicular to the line x - 18 = y/4 = z/6 - 6, we can use the formula for the equation of a plane:
A(x-x₁)+B(y-y₁)+C(z-z₁)=0
where (x₁, y₁, z₁) is a point on the plane and (A, B, C) is the normal vector to the plane. To find the normal vector, we can take the direction vector of the line and find its orthogonal vector. Then, we can substitute the values of the point and the normal vector into the equation to get the equation of the plane.