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In this paper, we obtain the intrinsic equations of some special curves in Euclidean 3-space characterized by det 
= 0, where r
i
< r
i+1,r
1 ∈ {1, 2, 3}, r
2 ∈ {2, 3, 4} and r
3 ∈ {3, 4, 5}.
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