A rectangular box is constructed in 3-space with one corner at the origin and other vertices at (1, 0, 0), (0, 4, 0), (0, 0, 2).

Question

Blababa [14]

3 years ago

7

A rectangular box is constructed in 3-space with one corner at the origin and other vertices at (1, 0, 0), (0, 4, 0), (0, 0, 2).

Find the length of the diagonal of the box.

Mathematics

1 answer:

77julia77 [94] · Answer 1 · 2021-12-06T09:35:15+03:00

The space diagonal will have length ...

... d = √(1² +4² +2²) = √(1 +16 +4) = √21

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This can be found using the Pythagorean theorem. A drawing can help. Find the length of any face diagonal, then use that length as the leg of a right triangle whose hypotenuse is the space diagonal and whose other leg is the edge length not used in the first calculation.