## You are here

Homedifference of vectors

## Primary tabs

# difference of vectors

Let $\vec{a}$ and $\vec{b}$ be two vectors in the plane (or in a vector space). The difference vector or difference $\vec{a}\!-\!\vec{b}$ of $\vec{a}$ and $\vec{b}$ is a vector $\vec{d}$ such that

$\vec{b}+\vec{d}=\vec{a}.$ |

Thus we have

$\displaystyle\vec{b}+(\vec{a}\!-\!\vec{b})=\vec{a}.$ | (1) |

According to the procedure of forming the sum of vectors by setting the addends one after the other, the equation (1) tallies with the picture below; when the minuend and the subtrahend emanate from a common initial point, their difference vector can be directed from the terminal point of the subtrahend to the terminal point of the minuend.

Remark. It is easily seen that the difference $\vec{a}\!-\!\vec{b}$ is same as the sum vector

$\vec{a}\!+\!(-\vec{b})$ |

where $-\vec{b}$ is the opposite vector of $\vec{b}$: it may be represented by the directed line segment from the terminal point of $\vec{b}$ to the initial point of $\vec{b}$.

## Mathematics Subject Classification

53A45*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections