Find the distance between the given parallel planes.4x − 5y + z = 16,    8x − 10y + 2z = 2

To find the distance between the given parallel planes, we can use the formula:

distance = |d| / √(a^2 + b^2 + c^2)

where d is the constant term in the equation of one of the planes, and a, b, and c are the coefficients of x, y, and z respectively.

In this case, the equations of the planes are:

4x - 5y + z = 16 8x - 10y + 2z = 2

We can see that the coefficients of x, y, and z are the same for both equations, which means the planes are parallel.

Let's calculate the distance between the planes:

For the first plane, the constant term is 16, and the coefficients are 4, -5, and 1 respectively.

Using the formula, we have:

distance = |16| / √(4^2 + (-5)^2 + 1^2) = 16 / √(16 + 25 + 1) = 16 / √42 = 16 / 6.4807 ≈ 2.47

Therefore, the distance between the given parallel planes is approximately 2.47 units.