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Straight Lines

Passes through a point & parallel to a vector

Equation for a line that:

  • passes through
  • is parallel to

Parametric equation

Symmetric equation

Passes through 2 points

Equation of a line passes through , . and are the position vectors of and .

Parametric equation

Symmetric equation

Normal to 2 lines

Let be two lines.

Here , are vectors parallel to respectively.

Normal to both lines: . Unit normal to both lines can be found by:

Angle between 2 straight lines

Using the lines mentioned above:

Here are vectors parallel to respectively.

Shortest distance to a point

Suppose and lie on a line. Shortest distance to the point is: