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A rectangular box is bounded by planes passing through the points (-1, 2, 5) and (1, -1, -1), each plane being parallel to one of the coordinate planes. What is the length of the space diagonal of this box?

1. 2
2. 3
3. 6
4. 7

Correct answer: 7

Solution

The opposite corners (-1,2,5) and (1,-1,-1) give edge lengths |1-(-1)|=2, |-1-2|=3, |-1-5|=6. The space diagonal is sqrt(2^2+3^2+6^2)=sqrt(49)=7.

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