[itex]\frac{}{}[/itex]Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I've been trying to search for a general description for the Euclidean distance from a point to a line formula in [itex]\mathbb{R}^n[/itex]. This line is assumed to be a straight line where a directional vector [itex]f \in \mathbb{R}^n[/itex] is constant and known, and a constant point on the line is known, [itex]y \in \mathbb{R}^n[/itex].

For the 2D and 3D cases this is quite simple. Given a point [itex]X_0 = (x_0,y_0,z_0)[/itex] the distance is [itex]\frac{|f \times (y - X_0)|}{|f|}[/itex] where the cross product is obvious for these cases.

I guess what I'm most unclear on is the cross product in higher dimensions and furthermore the euclidean distance in higher dimensions. I think a general understanding of one will eventually lead into the other.

Thanks for your help.

Best

S

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# Distance from a point to a line defined in R^N

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