Math
posted by sophie on .
What is the distance between the parallel planes 2x+y3z=13 and 2x+y3z=35?

Pick any point on the first plane, say,
(0,13,0)
distance from that point to
2x + y  3z  35 = 0
= 2(0) + 13  3(0)  35/√(2^2 + 1^2 + (3)^2)
= 22/√14 or after rationalizing , 11√14/7 
simple. Find a point on the first plane. When x and z are zero, y=13.
Now we find the distance between the point (0,13,0) and the second plane.
d= (2*0+1*133*0 35)/sqrt(4+1+9)
d= 13/sqrt(14)