# Point on plane closest to point in R3

1. Sep 6, 2010

### TsAmE

1. The problem statement, all variables and given/known data

Let P1 be the plane passing through the point A(5,-6,7) parallel to the xy-plane. Write down the coordinates of the point D on P1 which is closest to C(1,3,4).

2. Relevant equations

None.

3. The attempt at a solution

I am not sure how to attempt this problem. I tried sketching a diagram (attached), but didnt know what else to do.

File size:
9.7 KB
Views:
55
2. Sep 6, 2010

### ╔(σ_σ)╝

Have you tried deriving the equation of the plane P1 ?

The equation of a plane is given as follows
$$a(x-x_{0}) + b(y-y_{0}) +c(z-z_{0}) =0$$
(a,b,c) is a normal vector to the plane.

It turns out that the distance between a point and a plane is shortest when the point is orthogonal to the plane.

3. Sep 7, 2010

### hunt_mat

It's a trick question. You know that the shortest distance from a point to a plane is in the normal direction to that plane. what is the normal to the plane they defined?

4. Sep 7, 2010

### TsAmE

Thanks, I figured it out D(1,3,7) :)