# Vector Subtraction/Examples/Example 1

## Examples of Vector Subtraction

Let:

 $\ds \mathbf a$ $=$ $\ds 6 \mathbf i + 4 \mathbf j + 3 \mathbf k$ $\ds \mathbf b$ $=$ $\ds 2 \mathbf i - 3 \mathbf j - 3 \mathbf k$

Then:

$\mathbf a - \mathbf b = 4 \mathbf i + 7 \mathbf j + 6 \mathbf k$

## Proof

By definition:

$\mathbf a - \mathbf b = \mathbf a + \paren {-\mathbf b}$

Summing $\mathbf a$ and $-\mathbf b$ by components:

 $\, \ds x: \,$ $\ds \paren {6 + \paren {-2} } \mathbf i$ $=$ $\ds 4 \mathbf i$ $\, \ds y: \,$ $\ds \paren {4 + \paren {-\paren {-3} } } \mathbf j$ $=$ $\ds 7 \mathbf j$ $\, \ds z: \,$ $\ds \paren {3 + \paren {-\paren {-3} } } \mathbf k$ $=$ $\ds 6 \mathbf k$

$\blacksquare$