Thread: Find the equation of the level surface through (-1,2-1)

Hi,

The question is: Find the eq. of the level surface through point p= (1,2,-1) and find the eq of the straight line in R3 which is normal to this surface at p

Is finding the equation of the level surface to f(x,y,z) = x^2 - y^2 + z^2 at point (-1,2,-1) the same as finding the equation of the tangent plane to the surface at that point?

Thanks for any help!

Originally Posted by Ant

The question is: Find the eq. of the level surface through point p= (1,2,-1) and find the eq of the straight line in R3 which is normal to this surface at p

Is finding the equation of the level surface to f(x,y,z) = x^2 - y^2 + z^2 at point (-1,2,-1) the same as finding the equation of the tangent plane to the surface at that point?

No it is not. It simply means writing the equation where is a constant.

So in this case we have .

So here we have ?

I also have that the equation to of the straight line normal to this surface at p is:

where t is a scalar variable.

Can anyone say if i'm on the right track here? Thanks

Originally Posted by Ant

I also have that the equation to of the straight line normal to this surface at p is:

where t is a scalar variable.

Can anyone say if i'm on the right track here? Thanks

You forgot the point:

Of course! Thanks again