- Find the equation of the plane tangent to the unit sphere at the point (1/ √3, 1/ √3, 1/ √3). (Hint: think about the sphere geometrically to find the normal direction to the plane.) Describe the intersection of this plane with z=3
- Find the equation of the plane tangent to the unit sphere at the point (1/ √3, 1/ √3, 1/ √3). (Hint: think about the sphere geometrically to find the normal direction to the plane.) Describe the intersection of this plane with z=3
Do you know how to write the equation of a plane when you know a point on the plane and the direction of the normal to the plane?
This is the situation you have here. The normal at your given point points directly towards (or away from) the origin.