Final answer:
To find the equation of the plane that passes through three given points, we can use the formula for the equation of a plane in 3D space.
Step-by-step explanation:
To find an equation of the plane that passes through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0), we can use the formula for the equation of a plane in 3D space. The formula is given as (x - x1)(y2 - y1)(z3 - z1) - (x2 - x1)(y - y1)(z3 - z1) + (x2 - x1)(y2 - y1)(z - z1) = 0, where (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) are three points on the plane. Plugging in the given points, we have (x - 0)(9 - 9)(0 - 9) - (9 - 0)(y - 9)(0 - 9) + (9 - 0)(9 - 9)(z - 9) = 0, which simplifies to -9(y - 9) + 9(z - 9) = 0. This is the equation of the plane that passes through the given points.