Final answer:
The equation of the plane through P0(5,5,-7) with normal vector (2,-1,4) is 2x - y + 4z = -43.
Step-by-step explanation:
To find the equation of the plane, we can use the formula:
Ax + By + Cz = D
where (A, B, C) is the normal vector and (x, y, z) are the coordinates of a point on the plane.
In this case, the normal vector is (2, -1, 4), and a point on the plane is (5, 5, -7). Plugging these values into the equation, we get:
2x - y + 4z = D
To find the value of D, we can substitute the coordinates of the given point:
2*5 - (-1)*5 + 4*(-7) = D
Simplifying, we get D = -43. Therefore, the equation of the plane is:
2x - y + 4z = -43