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Mathematics · Glossary

What is Direction vector?

Definition 15.8 High School Mathematics · Chapter 15 — Vectors and Lines in the Plane

A direction vector of a line dd is any nonzero vector u⃗\vec u such that AB→\vect{AB} is collinear with u⃗\vec u for all points A,BA, B of dd.

The line x - 3y + 5 = 0 of , its direction vector u = AB (red, here scaled by 1/2), and the two points used to build the equation.
The line x−3y+5=0x - 3y + 5 = 0 of Example 15.11, its direction vector u⃗=AB→\vec u = \vect{AB} (red, here scaled by 12\frac12), and the two points used to build the equation.
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