Tangent Vectors to Curves

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The idea of tangent vectors to curves is looked at along with the ideas of null and non-null curves.
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Thanks. Ha, the photon moves in the 3d space fast like hell, but the time always drags it back. What I don't get, the space-time is 4-dimensional, but the caclulation of the e vectors (dr/dx) and the metric tensor assumes an (at least 5D) ambient space, so somehow they always work around this problem.

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I don't know what null curve is.
Can you show me the visual image of null curve, please?

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