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In this paper, we investigate the tangent indicatrix of the curve C withconstant curvature. Tangent indicatrix of the curve C is characterized withdet(C^(3),C^(4),C^(5))=0 in Minkowski 3-space E13. Moreover, we study nullslant helices using the determinant approach and give the followingcharacterization: A curve C is a null slant helix in E13 if and only ifdet(C^(3),C^(4),C^(5))=0. Then similar results are obtained for non-null curveswith the condition k=1.

Geometric Interpretation of det(C^(3),C^(4),C^(5))=0 in E13