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В кубе ABCDA1B1C1D1ABCDA_1B_1C_1D_1, ребро которого 6\sqrt{6}, найдите расстояние от точки CC до прямой BD1BD_1

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Full solution

Q. В кубе ABCDA1B1C1D1ABCDA_1B_1C_1D_1, ребро которого 6\sqrt{6}, найдите расстояние от точки CC до прямой BD1BD_1
  1. Cube Edge Length: In cube ABCDA1B1C1D1ABCD A_1 B_1 C_1 D_1, all edges are equal. The edge length is given as 6\sqrt{6}.
  2. Distance Calculation: To find the distance from point CC to line BD1BD_1, we can use the diagonal of face ABCDABCD, which is the hypotenuse of a right triangle with legs equal to the edges of the cube.
  3. Diagonal Length Calculation: The length of the diagonal of face ABCD is (62+62)=(36+36)=72=62\sqrt{(6^2 + 6^2)} = \sqrt{(36 + 36)} = \sqrt{72} = 6\sqrt{2}.

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