From the equation we get and so can write the "position vector" of any point on the surface in terms of x and y only:
The derivatives of that vector with respect to x and y, evaluated at (1, 2, 15), will be independent tangent vectors.
I hesitated to put this in calculus but oh well.
We have a surface and a point belonging to that surface.
I was asked to find the normal vector, which I did (its (5;12;-1) ). I am also asked to find vectors linearly independant and tangent to that S surface.
By using partial derivatives I have found
I don't know how to find the vectors from that point. I know that 5 is the slope for the partial derivative in x and 12 is the slope for the partial derivative in y.
Thanks for the help!