ralucacoriciuc6146 ralucacoriciuc6146
  • 04-09-2019
  • Mathematics
contestada

consider a unit cube with one one corner at the origin what is the angle between any two diagonals?

Respuesta :

aramisdegaula1977
aramisdegaula1977 aramisdegaula1977
  • 08-09-2019

Answer:

1.231 rad

Step-by-step explanation:

Suppose that the vertex opposite the origin is (a, a, a), therefore, the geometric vector A = (a, a, a) is a diagonal of the cube. There are two opposite vertices (0, a, 0) and (a, 0, a), with which B = (a, 0, a) - (a, 0, a) = (a, -a, a) is the diagonal that intersects the first diagonal.

Now, [tex]\theta = arccos(\frac{A\bullet B}{\left\| A \right\| \left\| B \right\|}) = arccos(\frac{a^2}{3a^2}) = arccos(\frac{1}{3}) = 1.231 rad[/tex]

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