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Example:Finding Equation of a Line Parallel to Vector

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# Parallel (geometry)

Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not intersect or meet are called parallel lines.

http://en.wikipedia.org/wiki/Parallel_(geometry)

Line (geometry)

The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects. Thus, until seventeenth century, lines were defined like this: "The line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...] will leave from its imaginary moving some vestige in length, exempt of any width. [...] The straight line is that which is equally extended between its points"

A line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its end points. Depending on how the line segment is defined, either of the two end points may or may not be part of the line segment. Two or more line segments may have some of the same relationships as lines, such as being parallel, intersecting, or skew.

### Vector equation

The vector equation of the line through points A and B is given by r = OA + λ AB (where λ is a scalar multiple)

If a is vector OA and b is vector OB, then the equation of the line can be written: r = a + λ (b - a)

A ray starting at point A is described by limiting λ≥0

(Our solved example in mathguru.com uses this concept)

http://en.wikipedia.org/wiki/Line_(geometry)