00:01
Okay, so we have two planes here.
00:01
The first one is x plus y plus z is equal to zero, and then the second one is x plus 5y plus 2z is equal to one.
00:12
So we can get the normal vector to each of the planes, just taking the coefficients because we have their standard form equation.
00:21
So here all the coefficients are one.
00:23
So we have one, one, and one.
00:26
And then here we have 1, 5, comma, 2.
00:29
Now, if we want to find the angle between the planes, that's the same thing as the angle between their normal vectors, because you're just shifting by 90 degrees.
00:37
Or, you know, you could be working on the same relative distance between them or angle between them in just two different orientations.
00:48
So we can just work with the normal vectors.
00:50
And then that simplifies, the problem simplifies now, instead of finding an angle between two planes, we're finding an angle between two vectors.
00:57
Specifically, the cosine of the angle.
00:58
So we don't even have to have to have to have.
00:59
To take that last step.
01:01
So by the law of cosines, the cosine of an angle between two vectors is going to be the dot product of the vectors divided by the product of their components...