Vector Sum/Component Definition/Examples/Example 1

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Examples of Vector Sum: Definition by Components

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:

$\mathbf a + \mathbf b = 8 \mathbf i + \mathbf j$


Proof

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

\(\, \ds x: \, \) \(\ds \paren {6 + 2} \mathbf i\) \(=\) \(\ds 8 \mathbf i\)
\(\, \ds y: \, \) \(\ds \paren {4 + \paren {-3} } \mathbf j\) \(=\) \(\ds \mathbf j\)
\(\, \ds z: \, \) \(\ds \paren {3 + \paren {-3} } \mathbf k\) \(=\) \(\ds 0 \mathbf k\)

$\blacksquare$


Sources