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110 lines
5.0 KiB
HTML
110 lines
5.0 KiB
HTML
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<h1 class="center">Unit Vector</h1>
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<p> </p>
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<p>A <a href="vectors.html">vector</a> has <b>magnitude</b> (how long it is) and <b>direction</b>:</p>
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<p class="center"><img src="images/vector-mag-dir.svg" alt="vector magnitude and direction" /></p>
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<h2>Unit Vector</h2>
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<p>A <b>Unit Vector</b> has a magnitude of <b>1</b>:</p>
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<p class="center"><img src="images/vector-unit.svg" alt="unit vector" /></p>
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<p> </p>
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<table border="0" align="center">
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<tr>
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<td align="center">The symbol is usually a lowercase<br />
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letter with a "hat", such as:</td>
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</tr>
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<tr>
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<td align="center"><img src="images/vector-unit-hat.gif" width="95" height="59" alt="vector a-hat" /></td>
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<tr>
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<td align="center">(Pronounced "a-hat")</td>
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</table>
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<h2>Scaling</h2>
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<p>A vector can be "scaled" off the unit vector. Here vector <b>a</b> is shown to be 2.5 times a unit vector. Notice they still point in the same direction:</p>
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<p class="center"><img src="images/vector-unit-scale.gif" width="262" height="199" alt="vector unit scale 1 to 2.5" /></p>
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<h2>In 2 Dimensions</h2>
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<p> Unit vectors can be used in 2 dimensions:</p>
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<p class="center"><img src="images/vector-unit-2d.gif" width="192" height="213" alt="vector a = 2x + 1.3y" /></p>
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<p>Here we show that the vector <b>a</b> is made up of 2 "x" unit vectors and 1.3 "y" unit vectors.</p>
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<h2>In 3 Dimensions</h2>
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<p>Likewise we can use unit vectors in three (or more!) dimensions:</p>
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<p class="center"><img src="images/vector-unit-3d.gif" width="200" height="162" alt="vector unit 3d" /></p>
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<script type="text/javascript">getQ(3044, 3045, 3046, 3047, 3048, 3049, 3909, 3910, 3911, 3912);</script>
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<a href="vectors.html">Vectors</a>
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<a href="index.html">Algebra Index</a>
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