00:01
Ok, so in this exercise we want to find the equation of the plan containing the point p equal to 0, negative 1, 3 and containing the vector a equal to 4, 1, 2 and the vector b equal to negative 6, 4, 3.
00:25
Ok, well, how can we find the equation of this plan? well, this is pretty easy.
00:32
Clearly, the normal vector to the plan passing through the point p and containing these two vectors, well, the normal vector is going to be the vector product of a and b.
00:48
So we need to compute this vector product.
00:51
Well, this one is going to be the determinant of the matrix i, j, k, 4, 1, 2, the vector a and the last row is going to be the vector b, negative 6, 4, 3.
01:09
Ok, let's compute this determinant.
01:11
Well, the first coordinate is going to be 3 minus 8, negative 5.
01:18
The second coordinate is going to be negative 1 multiplied by, ok, 12 plus 12, 24...