Trigonometry

I

ikmalamki

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Points P and Q are the two opposite vertices of a cube with an edge length 6. Two balls of radii 1 and 2 are inside of the cube. One of them touches all the three faces of the cube containing P and another touches all the three faces containing Q. Find the distance between the balls' centers.
 
If point P is at the origin, what are the co-ordinates of point Q?

What might you do next?
 
How long is the diagonal of the cube, PQ?

How far is the center of each ball from P or Q?
 
ikmalamki said:
please correct me.
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Nice first try. You should have included this in the very first post.

You have overlooked that your spheres do NOT go all the way to their respective corners.
 
ikmalamki said:
oke i understand, so center of each ball is
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That doesn't mean what you think it means. P and Q are points, not numbers.

But those are the distances of the centers from P and Q, respectively. So how far are the centers from each other?

(By the way, post #3 gave a hint at what would turn out to be an easier approach overall, but we're well on the way to an answer.)
 
Dr.Peterson said:
That doesn't mean what you think it means. P and Q are points, not numbers.

But those are the distances of the centers from P and Q, respectively. So how far are the centers from each other?

(By the way, post #3 gave a hint at what would turn out to be an easier approach overall, but we're well on the way to an answer.)
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this is true ?
 

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I agree with Dr. Peterson that you are close enough to a solution that there is no point NOW in using analytic geometry, but what it would have kept firmly in your mind is that you are dealing with three dimensions rather than two. A two dimensional diagram may hide something that is relevant.
 
You've got the wrong distances to P and Q, probably for the reason JeffM was concerned about.

Have you noticed that each ball's center can be thought of as being at the opposite corner of a small cube from P or Q?

Have you noticed that, as a result, each of those centers lies on the diagonal?

If not, then you may need to revert to the coordinate approach, which may require less visualization.
 
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