Question

find the unit vector perpendicular to x²+y²-z²=100​

Answer 1

Answer:

Write f(x,y,z) = z - x^2 - y^2

Explanation:

Write f(x,y,z) = z - x^2 - y^2 and take the partial derivatives if f w.r.t. x, y and z to get the i, j and k components of the normal vector at (x, y z).

N(x,y,z) = -2x i - 2y j + k. Evaluate at (0,1,1) to get N(0,1,1) = -2 j + k. To make it unit length, divide each component by sqrt(5).

unit outward normal at (0, 1, 1) = -2/sqrt(5) j + 1/sqrt(5) k. (It is also correct to write its negative, but it will be the inward pointing