# Point on plane closest to point in R3

## Homework Statement

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).

None.

## 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.

#### Attachments

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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.

hunt_mat
Homework Helper
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?

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