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Home Vectors Vectors and Lines in Space Corollary 2
 
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Corollary 2

COROLLARY 2

Two points in space determine a line. The line through A and B has the vector equation

X = A + t(B - A).

PROOF

A line L passes through A and B if and only if A is a position vector of L and B - A is a direction vector of L. By Theorem 2, this happens if and only if L is the line with the vector equation X = A + t(B - A).

Example 5: A Line Through Two Points

The formula ½(A + B) for the midpoint of the line segment AB holds for three as well as two dimensions.

Example 6: Finding The Midpoint Of A Line Segement

Home Vectors Vectors and Lines in Space Corollary 2

Last Update: 2006-11-05