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:

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

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: \, $

$\ds \paren {3 + \paren {-\paren {-3} } } \mathbf k$

$=$

$\ds 6 \mathbf k$

$\blacksquare$

1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.1$ Definitions, Elementary Approach: Example $1.1.1$