Help : Perpendicular distance of the plane

[ahgang]

Homework Statement

Find the perpendicular distance of the plane 5x+2y-z=-22 from the origin O by first finding the co-ordinates of the point P on the plane such that OP is perpendicular to the given plane.

Homework Equations

It only given plane vector,how i going to figure out the perpendicular distance?

The Attempt at a Solution

I really don't know where to start.Can help to elaborate?

Thanks

 

[sandy.bridge]

Set x and y equal to zero, solve for z. The perpendicular distance will be the absolute value of this number.

 

[ahgang]

Set x and y equal to zero, solve for z. The perpendicular distance will be the absolute value of this number.

You mean (X,Y.Z) = (0.0.Z)?Then minus the plane location?

 

[hotvette]

One option is to use Lagrange Multipliers to get the coordinates of the point by treating it as a minimization problem (i.e. distance from origin to an arbitrary point) with the constraint that the arbitrary point must lie on the plane. Hint: minimizing the square of the distance also minimizes the distance.

 

[gneill]

You should be able to write a normal to the plane by inspection of the defining equation. Any line that is perpendicular to the plane must be parallel to this normal. So write a parametric equation of a line that passes through the origin that lies along this normal vector. Where does this line intersect the plane?