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The shortest distance from the plane ...

The shortest distance from the plane `12 x+4y+3z=327` to the sphere `x^2+y^2+z^2+4x-2y-6z=155` is a. `39` b. `26` c. `41-4/(13)` d. `13`

A

39

B

26

C

`41(4)/(13)`

D

13

Text Solution

AI Generated Solution

To find the shortest distance from the plane \(12x + 4y + 3z = 327\) to the sphere \(x^2 + y^2 + z^2 + 4x - 2y - 6z = 155\), we will follow these steps: ### Step 1: Find the center and radius of the sphere The equation of the sphere is given as: \[ x^2 + y^2 + z^2 + 4x - 2y - 6z = 155 \] ...
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