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From Vector to Line

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Any nonzero vector defines a unique perpendicular line in 2D. Except for lines through the origin, every line defines a nonzero vector. Hover over the blue line to see the equation of the line generated by the movable point.

Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA

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The vector is in standard position, starting at the origin. The line passes through the tip of the vector.

Conversely, a line determines the vector from the origin to the closest point to the line from the origin.

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