00:01
Hello, my name is christina, and in this lesson we will determine the parametric equation for the line tangent to the curve of intersection of the surfaces at the given point.
00:17
So let's assume f x, y z is given by this equation, and g x, y z, equal to x, our point, p0 is given by coordinates 1, 1 ,1.
00:46
The first step is to find the gradient of f, and for this we need the first derivative of f with respect to each of its variables.
00:59
So fx is 1, fy is 2y, and fz is 2.
01:14
The gradient of f in our point, 1 -1 -1 is equal to i plus 2j plus 2k.
01:32
We will do the same for our surface g.
01:40
So g x is equal to 1, gy is equal to 0, gz is equal to 0, so our gradient for surface g1 -1 -1 is equal to i...