How do I do vector subtraction?

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How do I do vector subtraction?

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Answer 1 · 2014-12-30T20:47:35

Given two vectors $\to v$ $vecv$ and $\to w$ $vecw$ you have:
$\to v - \to w = \to v + (- \to w)$ $vecv-vecw=vecv+(-vecw)$

Graphically we can use the Parallelogram Law:
enter image source here

If you have the vectors in components form you again use:
$\to v - \to w = \to v + (- \to w)$ $vecv-vecw=vecv+(-vecw)$ operating on each set of corresponding components.

For example:
$\to v = 4 \to i + 2 \to j - 5 \to k$ $vecv=4veci+2vecj-5veck$ and:
$\to w = - 2 \to i + 4 \to j + \to k$ $vecw=-2veci+4vecj+veck$

$\to v - \to w = \to v + (- \to w) = [4 + (2)] \to i + [2 + (- 4)] \to j + [- 5 + (- 1)] \to k =$ $vecv-vecw=vecv+(-vecw)=[4+(2)]veci+[2+(-4)]vecj+[-5+(-1)]veck=$
$= 6 \to i - 2 \to j - 6 \to k$ $=6veci-2vecj-6veck$

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How do I do vector subtraction?

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