# Vector Difference

A **vector difference** is the result of subtracting one vector from another vector.

The difference of vectors v and u is written v-u using the normal minus sign.

$$ v - u $$

The vector difference v-u is equivalent to the sum vector v + (- u) where -u is the negative vector of the vector u.

$$ v + (-u) $$

The difference v-u is a vector in R^{n} obtained by subtracting the corresponding components of v and u.

**Example**

Given two vectors

$$ v = \begin{pmatrix} 2 \\ 1 \end{pmatrix} $$

$$ u = \begin{pmatrix} 1 \\ 4 \end{pmatrix} $$

the difference v-u is the vector

$$ v - u = \begin{pmatrix} 2 \\ 1 \end{pmatrix} - \begin{pmatrix} 1 \\ 4 \end{pmatrix} = \begin{pmatrix} 2-1 \\ 1-4 \end{pmatrix} = \begin{pmatrix} 1 \\ -3 \end{pmatrix} $$

The vector difference drawn from the head of the second vector (u) to the head of the first vector (v)