00:01
In this problem, we want to determine the acute angle between the following two planes.
00:08
So we have one plane equation, x minus y plus z equal to 5, and the second, 2x plus, i'm assuming this is a y here, plus y minus 2z.
00:24
So what do they mean by acute angle between planes? so let's say we have our first plane, p1, and our second plane, p2.
00:42
These two planes intersect at an angle.
00:44
We want to determine the smallest angle.
00:52
How can we do this? what we need to understand is that planes are described by their normal vector.
01:00
So this is n2, the normal vector 2p2, and this here is, i'll draw them in red and blue.
01:11
This normal vector is n1, and this normal vector is n2.
01:22
And the angle between these two vectors will be our acute angle.
01:30
Let's find n1 and n2.
01:32
So generally speaking, planes write in the form ax plus by plus c equal to zero, where the coefficients a, b, c correspond to the normal vector...