00:01
In this question, we are given a point 0 .00 and a plane, this is the equation on the plane, we want to find the shortest distance of this point to the plane.
00:10
Now, in general, if i have a plane with a normal vector, abc, so my equation on the plane will be a x plus b y plus cz plus d is equal to 0.
00:27
And if i have a point p on the plane and a point q somewhere in space, i'm interested to find this shortest distance to the blink.
00:39
So let me call this d.
00:41
So we will actually find the vector pq in order to find the shortest distance d.
00:50
So d is pq dot with the normal vector.
00:58
We want the positive value, so we mod it.
01:02
Divided by the magnitude of the normal vector.
01:06
So as you can see, our point 0 .00 will be over here.
01:13
And our normal vector will be 8 minus 4, 1.
01:19
So i'm going to replace this with 8 minus 4 .1.
01:28
And so this one is 8 minus 4 1 is equal to 8.
01:45
So that's the occasion of plane.
01:47
Now, so all it left for us to do is to find a point p on the plane.
01:53
Now, to find this point p, all we need to do is to guess a point and to sub it into here.
02:05
See whether we'll get 8 on the right side...