Final answer:
To find the equation of the plane through the point P(5,3,3) and parallel to the plane 2y - 2x + 3z = 10, we can use the fact that parallel planes have the same normal vector.
Step-by-step explanation:
To find the equation of the plane through the point P(5,3,3) and parallel to the plane 2y - 2x + 3z = 10, we can use the fact that parallel planes have the same normal vector. The normal vector for the given plane is (-2, 2, 3). So, the equation of the plane through P is given by:
2*(-2)(x - 5) + 2*(2)(y - 3) + 3*(z - 3) = 0
This simplifies to -4x + 4y + 6z - 22 = 0.