Hello, kingkaisai2!

You've been asked toderivethis distance formula . . .messy!

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: P_1P_2)^2\:=\p + aT - p)^2 + (q + bT - q)^2 +" alt="D^2\:=\P_1P_2)^2\:=\p + aT - p)^2 + (q + bT - q)^2 +" />

. . . .

Since

. . we have: .

Hence: .

Therefore: .