) If the gradient of ff is ∇f=xi⃗ +yj⃗ +3zyk⃗ ∇f=xi→+yj→+3zyk→ and the point P=(−6,−6,−2)P=(−6,−6,−2) lies on the level surface f(x, y,z)=0f(x, y,z)=0, find an equation for the tangent plane to the surface at the point PP.

-3x-3y-z=38

Step-by-step explanation:

To find the equation of the tangent plane you can use

the point P is (-6,-6,-2). Hence you have

hope this helps!!

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.