maximum distance from point to sphere

**harriette** · January 31st 2011, 03:24 PM

I have to calculate the maximum distance from the point $T(1, -1, 3)$ to the sphere $x^2+y^2+z^2-6x+4y-10z-62=0$ .

Here's what I did.
The equation for the sphere is $(x-3)^2+(y+2)^2+(z-5)^2=100$ .
That means the center of the sphere is $C(3, -2, 5)$ , and the radius is $r=10$ .
I think the maximum distance $d_m$ is the distance from the point $T$ to the center of the sphere plus the radius:
$d_m=d(T, C)+r$ .

Is this okay?
Please advise.
Thank you!

**Ackbeet** · January 31st 2011, 03:34 PM

Everything looks good so far. What do you get?

**harriette** · January 31st 2011, 03:39 PM

I get
$d((1, -1, 3), (3, -2, 5))=\sqrt((3-1)^2+(-2+1)^2+(5-2)^2 )=\sqrt(9)=3$ so $d_m=3+10=13$ .

It seems too simple, are you sure I'm not thinking something terribly wrong?

Thank you for your quick reply!

**Ackbeet** · January 31st 2011, 03:49 PM

You're not computing the distance formula correctly. It should be more like

$\sqrt{(3-1)^2+(-2+1)^2+(5-2)^2}=\sqrt{4+1+9}=\sqrt{14}.$

[EDIT]: Ignore this post. See below for correction.

**harriette** · January 31st 2011, 03:52 PM

Why do we have (5-2)^2 instead of (5-3)^2? I'm afraid I don't understand.

**Ackbeet** · January 31st 2011, 03:56 PM

I'm sorry. You're correct. It should be 3, like you got.

**harriette** · January 31st 2011, 03:57 PM

Thank you so much! I'm quite insecure when I'm doing the exercises on my own, it really helps when someone checks your work.

**Ackbeet** · January 31st 2011, 04:25 PM

If you feel insecure when you're doing exercises, I would come up with a system of checks you can run against your answers to justify them to yourself. It's good problem-solving strategy anyway.

You're very welcome. Have a good one!

Thread: maximum distance from point to sphere

LinkBack

Thread Tools

Display

maximum distance from point to sphere

Similar Math Help Forum Discussions

Curve's point A tangent line passes through a point P. What is the distance of AP

Using a normal vector and point to find distance and the closest point

Finding point on sphere furthest from point in space

distance between a pt. to sphere

Calculating coords of a point on a straight line at a distance from start point...

Search Tags