Question

given xy^2 - x^2y + z^3 = 0 and the plane is modeled by x + y + z = 3. find the vector model for the tangent line at the point (1, 1, 1)

Answer 1

my first idea would be to find where the plane and the eqaution intersect

Answer 2

okay so be setting Fx = x, Fy = y, and Fz = z?

Answer 3

F = xy^2 - x^2y + z^3

N = <y^2 -2xy , 2xy -x^2, 3z^2>
= <1-2 , 2-1, 3>
= <-1,1,3>

while this gives us a tells us the tangent plane at the point; we still need to cross it with the given planes normal to create a direction vector for the line created by the intersection of the 2 planes