Final answer:
To verify if the two planes are parallel, compare their normal vectors. If the normal vectors are the same, the planes are parallel. Use the formula for the distance between a point and a plane to find the distance between the two planes.
Step-by-step explanation:
To verify if the two planes are parallel, we need to compare their normal vectors. The normal vector of a plane in the form ax + by + cz = d is given by the coefficients (a, b, c). If the two planes have the same normal vector, then they are parallel. In this case, both planes have the equation 3x - 4z = k, where k is either 4 or 9. The normal vector for both planes is (3, 0, -4), so the planes are parallel.
To find the distance between the planes, we need to consider the distance between a point on one plane and the other plane. We can use the formula for the distance between a point and a plane, which is given by:
d = |Ax + By + Cz - D| / sqrt(A^2 + B^2 + C^2),
where (A, B, C) is the normal vector of the plane and D is the constant term. Plugging in the values for the first plane, we get:
d = |3x - 4z - 4| / sqrt(3^2 + 0 + (-4)^2) = |3x - 4z - 4| / 5.
For the second plane, we get:
d = |3x - 4z - 9| / sqrt(3^2 + 0 + (-4)^2) = |3x - 4z - 9| / 5.
Therefore, the distance between the planes is |4 - 9| / 5 = 5/5 = 1.