00:01
Okay, here i want to find the plane equation that contains the point one, two, three, and also contains the line given on the right here.
00:10
So, first step is to find two vectors which lie in the plane.
00:19
Now, i can write this as zero plus three t.
00:23
Here is one plus one t to minus one t.
00:28
So i know it wants a vector that lies in the plane.
00:31
It must be the vector 3 -1 negative 1.
00:44
So 3 -1 -negative 1 lies in the plane.
00:52
Now, this point also lies in the plane.
00:58
So i know that 0 -1 -2 is a point on the plane.
01:05
Let's call this one a here, this one b.
01:10
Let's find the vector ab.
01:12
A .v will be ob minus oa, so 0 minus 1, negative 1, 1 minus 2, negative 1, and 2 minus 3 also negative 1.
01:30
So may as well find ba, it's a bit neater.
01:33
B .a will be simply 1, 1, 1.
01:39
So a .b, b, a, both lie in the plane.
01:44
Now, next step, work out a vector at right angles to the plane.
01:48
In other words, find n the plane normal.
01:52
And to do that, i do cross product...