00:01
So in this question, i'm gonna find the point on the plane x minus two y plus three z is equal to 12, that is closest to the point zero, two, two.
00:08
Now, there are multiple ways to approach this question.
00:12
I'm gonna use the plane and line approach.
00:16
So in other words, i have some plane and i have a point and i'm trying to figure out what is the point on the plane that is closest, in this case, to zero, two, two.
00:31
What i'm gonna do is think about the perpendicular.
00:34
Now, what do i know about the direction of the perpendicular? the direction of the perpendicular is in the direction of the normal vector to the plane, which is one, negative two, three.
00:48
So what i'm gonna do is write the equation of the line passing through the point zero, two, two that is perpendicular to my plane.
00:59
That would be x equals zero plus one t and then y equals two minus two t and z equals two plus three t.
01:12
And then i plug in to my equation of the plane.
01:16
So i get t minus two times my y, which is two minus two t plus three times my z, which is two plus three t equals 12.
01:30
I'm getting t minus four plus four t plus six plus nine t equals 12...