Find the perpendicular distance of the point (p,q,r) from the plane ax+by+cz=d

Explain concisely please

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- Jul 24th 2006, 01:14 AMkingkaisai2The perpendicular distance-vector
Find the perpendicular distance of the point (p,q,r) from the plane ax+by+cz=d

Explain concisely please - Jul 24th 2006, 05:46 AMSoroban
Hello, kingkaisai2!

You've been asked to__derive__this distance formula . . .*messy!*

Quote:

Find the perpendicular distance of the point from the plane

We want a line from perpendicular to the plane.

The plane has normal direction:

So our line has parametric equations:

To find , the intersection of the line and the plane:

. . .

. . and solve for . . . call this

Then is: .

Let be the desired distance.

Then:

. . . .

Since

. . we have: .

Hence: .

Therefore: .