Final answer:
To find the implicit equation for the plane passing through the given points, calculate the normal vector to the plane using the cross product of two vectors. Then, use one of the given points and the normal vector to form the equation of the plane.
Step-by-step explanation:
To find the implicit equation for the plane passing through the points (3,4,2), (5,5,4), and (1,9,7), we can use the cross product of two vectors formed by subtracting one point from another. Let's consider the vectors formed by subtracting (3,4,2) from (5,5,4) and (3,4,2) from (1,9,7). These two vectors are perpendicular to the plane. Taking the cross product of these vectors will give us the normal vector to the plane. Finally, we can use one of the given points and the normal vector to form the equation of the plane in the form ax + by + cz = d.