# Differentiability and Tangent Plane

• Feb 17th 2013, 08:39 AM
apatite
Differentiability and Tangent Plane
find the x, y, and z intercepts of the plane tangent to the sphere of radius sqrt(14) with center at the origin, at the point (1,2,3)?
• Feb 17th 2013, 09:01 AM
Mathsdog
Re: Differentiability and Tangent Plane
You could start with the observation that the vector (1, 2, 3) is normal to the plane you need to find, and this, along with the fact that this point (1, 2, 3) is in the plane, determines the plane uniquely.
• Feb 17th 2013, 09:12 AM
Plato
Re: Differentiability and Tangent Plane
Quote:

Originally Posted by apatite
find the x, y, and z intercepts of the plane tangent to the sphere of radius sqrt(14) with center at the origin, at the point (1,2,3)?

I hope that you realize that this is not a homework service.
Therefore, you are expected to show some effort on your part.

If \$\displaystyle f=x^2+y^2+z^2-14\$, then the normal of the plane is \$\displaystyle \nabla f(1,2,3)\$.