<div style="padding:40px;color:#cbccc6"><h1>点积 / 叉积（2D）</h1><p>点积 = 投影长，叉积 = 平行四边形面积。</p><div style="padding:20px;background:#0d1017;border-left:3px solid #ffb454"><span class="katex-display"><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">c</span><span class="mord mathnormal">d</span><span class="mord mathnormal">o</span><span class="mord mathnormal">t</span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">∣</span><span class="mord mathnormal">a</span><span class="mord">∣∣</span><span class="mord mathnormal">b</span><span class="mord">∣</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">cos</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">t</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">t</span><span class="mord mathnormal">im</span><span class="mord mathnormal">es</span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">∣</span><span class="mord mathnormal">a</span><span class="mord">∣∣</span><span class="mord mathnormal">b</span><span class="mord">∣</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.6595em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">in</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">t</span><span class="mord mathnormal">a</span></span></span></span></span></div><p style="color:#707a8c">该页面需要 JavaScript 进行交互式可视化。</p></div>