You are here:

- Home
- Science
- Mathematics
- Advanced Math
- Linear Algebra

Advertisement

I have no idea what to do for this problem. Any help would be appreciated.

Consider the sphere S of radius 5 centred at (1, 0,2). Find the equation of the plane tangent to S at the point (5,-3,2).

Hint: To get started, draw this situation in 2D with a circle.

Questioner:Nick

Country:Quebec, Canada

Category:Advanced Math

Private:No

Subject:Linear Algebra

Question:

I have no idea what to do for this problem. Any help would be appreciated.

Consider the sphere S of radius 5 centred at (1, 0,2). Find the equation of the plane tangent to S at the point (5,-3,2).

Hint: To get started, draw this situation in 2D with a circle.

..............................................

The vector form of the equation of a plane is:

normalvector dot (<x,y,z> - <x0,y0,z0>) = 0

since the normal vector is, er.. normal to any vector in the plane. (duh...)

So take your <x0,y0,z0> to be (1,0,2), the point IN the plane, and

take the normal to be vector CP. (C is the center, P is the point of tangency.)

That should do it.

Advanced Math

Answers by Expert:

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.**Education/Credentials**

-----------