[Solved] Consider a cube, and its internal diagonal. Let it have a corner at the origin, and edges i, j, and k. What angle (degrees) does this diagonal


Question: Consider a cube, and its internal diagonal. Let it have a corner at the origin, and edges i, \(\mathbf{j}\), and \(\mathbf{k}\).

  1. What angle (degrees) does this diagonal make with an edge of the cube? (what angle does \(\mathbf{i}+\mathbf{j}+\mathbf{k}\) make with \(\mathbf{k}\) ?)
  2. Therefore what angle does the diagonal make with a face? (what angle does \(\mathbf{i}+\mathbf{j}+\mathbf{k}\) make with \(\mathbf{i}+\mathbf{j}\) ?)

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