# Distance of plane to origin

• November 15th 2006, 01:35 AM
Distance of plane to origin
Hi,

I am trying to determine the distance of the plane 5x+2y+z=10 from the origin? Thank you.
• November 15th 2006, 02:33 AM
malaygoel
Quote:

Hi,

I am trying to determine the distance of the plane 5x+2y+z=10 from the origin? Thank you.

there are two methods:
either use the direct formula
I will tell you the second method.

Imagine a point P on the plane.
Join O and P.
Find the drs of OP.
For OP to be the shortest distance botween two planes, OP should have the drs that the normal to the plane has.

Try it.
If you get stuck anywhere in between, I will you the solution.

Keep Smiling
Malay
• November 15th 2006, 04:53 AM
ThePerfectHacker
Quote:

Hi,

I am trying to determine the distance of the plane 5x+2y+z=10 from the origin? Thank you.

The standard equation of the plane is,
$5x+2y+z-10=0$
So the distance formula says, distance from origin is,
$\frac{|5(0)+2(y)+(0)-10|}{\sqrt{5^2+2^2+1^2}}$