Prove that the sum of three vectors determined by the diagonals of the three adjacent faces of a cube passing through the same corner, the vectors being directed from the corner, is twice the vector determined by the diagonal of the cube passing through the same corner.

Prove that the sum of three vectors determined by the diagonals of the three adjacent faces of a cube passing through the same corner, the vectors being directed from the corner, is twice the vector determined by the diagonal of the cube passing through the same corner.

Prove that the sum of three vectors determined by the diagonals of the three adjacent faces of a cube passing through the same corner, the vectors being directed from the corner, is twice the vector determined by the diagonal of the cube passing through the same corner.