The volume of the tetrahedron, the equations of whose faces are \( a_{i} x+b_{i} y+c_{i} z+d_{i}=0(i=1,2,3,4) \) is \( \left|\frac{\Delta^{3}}{6 D_{1} D_{2} D_{3} D_{4}}\right| \) where \( D_{1}, D_{2}, D_{3} \), and \( D_{4} \) are cofactors of \( d_{1}, d_{2}, d_{3} \) and \( d_{4} \) in \( \Delta=\left|\begin{array}{llll}a_{1} & b_{1} & c_{1} & d_{1} \\ a_{2} & b_{2} & c_{2} & d_{2} \\ a_{3} & b_{3} & c_{3} & d_{3} \\ a_{4} & b_{4} & c_{4} & d_{4}\end{array}\right| \)
If a plane makes a tetrahedron with the coordinate plane of constant volume \( 64 k^{3} \). The product of lengths of intercepts of the plane on the coordinate axis is
(a) \( 24 k^{3} \)
(b) \( 4 k^{3} \)
(c) \( 6 k^{3} \)
(d) \( 6 \times 64 k^{3} \)
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