Find the distance between the planes 8y - 12x + 4z= 20 and 10y - 15x + 5z= 20.
To solve, determine if the planes are parallel, coincident or if they intersect.
To do so, simplify each equation.
For plane 1,
`-12x + 8y +4z = 20`
divide both sides by the GCF which is 4.
And for plane 2,
divide both sides by the GCF too.
Since the simplified form of the two planes have same coefficients of x, y and z , but with different constants, this means that they are parallel.
So, to solve for the distance between parallel planes, apply the formula:
Rationalize the denominator.
Then, take the absolute value.
Hence, the distance between the given planes is `sqrt15/15` units.