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O(0, 0, 0) ; A(a, 0, 0) ; B(0, a, 0) ;
C(0, 0, a) ; P(a, a, a) ; L(0, a, a) ;
M(a, 0, a) and N(a, a, 0).
The direction ratios of the diagonals OP, AL, BM and CN are
(a, a, a) ; (−a, a, a) ; (a, −a, a) and (a, a, −a).
∴ direction cosines of OP, AL, BM and CN are
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