0
$\begingroup$

How can I find a vector which is a unit normal vector to the surface $3x^2-yz+ z^2 = 0$ at the point $(1, -4, -3)$?

$\endgroup$
0
$\begingroup$

Hint: $(\nabla F)(a, b, c)$ is a normal vector to the surface $F(x, y, z) = 0$ at the point $(a, b, c)$.

$\endgroup$
0
$\begingroup$

For a surface given by the equation $\phi(x, y, z) = 0$, a normal at the point $(x, y, z)$ is $\nabla \phi (x, y, z)$. So find the gradient of the LHS and evaluate it at the given point. Then normalize it by dividing it by its magnitude.

I'll update this answer with the final answer once you get it yourself.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.