I had the following problem on my test today and I supposedly got the wrong answer but I can't seem to find where I went wrong. Please let me know if you see an error in my work:
Find the distance between the given parallel planes: 4z = 6y - 2x (Plane A)
6z = 2 - 3x + 9y (Plane B)
Let x = y = 0 on plane 6z = 2 - 3x + 9
6z = 2
z = 3
Thus we have the point (0,0,3) and to find the distance between this point on Plane B and Plane A there is the formula:
absolute value( a(x0) + b(y0) + c(z0) - D ) / sqrt(a^2 + b^2 + c^2)
plane A has: a = 2, y = -6, z = 4, d = 0
so, i did 2(0) - 6(0) + 4(3) = 12 / sqrt( 4 + 36 + 16)
12 / sqrt(56) and further reduced to 6/sqrt(14)
the computer assignment says this is wrong... any help is greatly appreciated.
Thanks in advance.