find the distance from the sphere to the plane

Smily

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May 27, 2006
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find the distance from the sphere x^2+ y^2+ z^2+ 2x+ 6y- 8z= 0 to the plane 3x + 4y + z= 15
:roll:
thanks for any help you can give me
 
Smily said:
sphere x^2+ y^2+ z^2+ 2x+ 6y- 8z= 0

Here's a start.

Group and complete the squares:

(x+1)2+(y+3)2+(z4)2=26\displaystyle (x+1)^{2}+(y+3)^{2}+(z-4)^{2}=26

Center at (-1, -3, 4), radius 26\displaystyle \sqrt{26}
 
If Π\displaystyle \Pi is a plane with normal N\displaystyle N then if AΠ\displaystyle A \notin \Pi then the distance from A\displaystyle A to Π\displaystyle \Pi is given by D(Π;A)=PANN\displaystyle D(\Pi ;A) = \frac{{\left| {\vec{PA} \cdot N} \right|}}{{\left\| N \right\|}} where PΠ.\displaystyle P \in \Pi .
 
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