Place a dot on the origin.
A line that has a slope of

goes by this formula:

So "rise -2" and "run 3."
Rise -2 is basically go down 2, so go down 2 units from the origin. Run 3 means go right 3 units from (0, -2).
Draw a line through (3, -2) and (0, 0).
20 because when you divide 12 by 3/5 you get 20 use a calculator
The tangent to
through (1, 1, 1) must be perpendicular to the normal vectors to the surfaces
and
at that point.
Let
. Then
is the level curve
. Recall that the gradient vector is perpendicular to level curves; we have

so that the gradient of
at (1, 1, 1) is

For the surface
, we have

so that
. We can obtain a vector normal to
by taking the cross product of the partial derivatives of
, and evaluating that product for
:


Now take the cross product of the two normal vectors to
and
:

The direction of vector (24, 8, -8) is the direction of the tangent line to
at (1, 1, 1). We can capture all points on the line containing this vector by scaling it by
. Then adding (1, 1, 1) shifts this line to the point of tangency on
. So the tangent line has equation

I'm new to this but, I believe its negative. I might be wrong, but please correct me.
H because that would equal 2