Vector Subtraction/Examples/Example 1
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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:
\(\, \ds x: \, \) | \(\ds \paren {6 + \paren {-2} } \mathbf i\) | \(=\) | \(\ds 4 \mathbf i\) | |||||||||||
\(\, \ds y: \, \) | \(\ds \paren {4 + \paren {-\paren {-3} } } \mathbf j\) | \(=\) | \(\ds 7 \mathbf j\) | |||||||||||
\(\, \ds z: \, \) | \(\ds \paren {3 + \paren {-\paren {-3} } } \mathbf k\) | \(=\) | \(\ds 6 \mathbf k\) |
$\blacksquare$
Sources
- 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.1$ Definitions, Elementary Approach: Example $1.1.1$