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6.3.2 平面向量的正交分解及坐标表示 - 版本历史
2026-05-05T16:00:23Z
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2024-04-18T15:06:21Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[6.3 平面向量基本定理及坐标表示]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[6.3 平面向量基本定理及坐标表示]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==知识要点==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==知识要点==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* 在平面直角坐标系中，设与$x$轴、$y$轴方向相同的两个单位向量分别为$\vec{i},\vec{j}$，取$\{\vec{i},\vec{j}\}$作为基底. 对于平面内的任意一个向量$\vec{a}$，由平面向量的基本定理可知，有且只有一对实数$x,y$，使得$\vec{a}=x\vec{i}+y\vec{j}$，我们把有序数对$(x,y)$叫做向量$\vec{a}$的坐标，记作$\vec{a}=(x,y)$<del style="font-weight: bold; text-decoration: none;">，</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* 在平面直角坐标系中，设与$x$轴、$y$轴方向相同的两个单位向量分别为$\vec{i},\vec{j}$，取$\{\vec{i},\vec{j}\}$作为基底. 对于平面内的任意一个向量$\vec{a}$，由平面向量的基本定理可知，有且只有一对实数$x,y$，使得$\vec{a}=x\vec{i}+y\vec{j}$，我们把有序数对$(x,y)$叫做向量$\vec{a}$的坐标，记作$\vec{a}=(x,y)$<ins style="font-weight: bold; text-decoration: none;">，其中，</ins>$x$叫做$\vec{a}$在$x$轴上坐标，$y$叫做$\vec{a}$在$y$轴上坐标，上式叫做$\vec{a}$的坐标表示.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">其中，</del>$x$叫做$\vec{a}$在$x$轴上坐标，$y$叫做$\vec{a}$在$y$轴上坐标，上式叫做$\vec{a}$的坐标表示.</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 在直角坐标平面内，以$O$为起点的向量$\overrightarrow{OA}$的坐标就是终点$A$的坐标.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 在直角坐标平面内，以$O$为起点的向量$\overrightarrow{OA}$的坐标就是终点$A$的坐标.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==例题==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==例题==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==练习==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==练习==</div></td></tr>
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2024-04-18T15:06:05Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2024年4月18日 (四) 23:06的版本</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[6.3 平面向量基本定理及坐标表示]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[6.3 平面向量基本定理及坐标表示]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==知识要点==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==知识要点==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* 在平面直角坐标系中，设与$x$轴、$y$轴方向相同的两个单位向量分别为$\vec{i},\vec{j}$，取$\{\vec{i},\vec{j}\}$作为基底. 对于平面内的任意一个向量$\vec{a}$，由平面向量的基本定理可知，有且只有一对实数$x,y$，使得$\vec{a}=x\vec{i}+y\vec{j}$，我们把有序数对$(x,y)$叫做向量$\vec{a}$的坐标，记作<del style="font-weight: bold; text-decoration: none;">$</del>$\vec{a}=(x,y)$<del style="font-weight: bold; text-decoration: none;">$</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* 在平面直角坐标系中，设与$x$轴、$y$轴方向相同的两个单位向量分别为$\vec{i},\vec{j}$，取$\{\vec{i},\vec{j}\}$作为基底. 对于平面内的任意一个向量$\vec{a}$，由平面向量的基本定理可知，有且只有一对实数$x,y$，使得$\vec{a}=x\vec{i}+y\vec{j}$，我们把有序数对$(x,y)$叫做向量$\vec{a}$的坐标，记作$\vec{a}=(x,y)$<ins style="font-weight: bold; text-decoration: none;">，</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>其中，$x$叫做$\vec{a}$在$x$轴上坐标，$y$叫做$\vec{a}$在$y$轴上坐标，上式叫做$\vec{a}$的坐标表示.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>其中，$x$叫做$\vec{a}$在$x$轴上坐标，$y$叫做$\vec{a}$在$y$轴上坐标，上式叫做$\vec{a}$的坐标表示.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 在直角坐标平面内，以$O$为起点的向量$\overrightarrow{OA}$的坐标就是终点$A$的坐标.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 在直角坐标平面内，以$O$为起点的向量$\overrightarrow{OA}$的坐标就是终点$A$的坐标.</div></td></tr>
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2024-04-18T14:17:34Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2024年4月18日 (四) 22:17的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3">第3行：</td>
<td colspan="2" class="diff-lineno">第3行：</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 在平面直角坐标系中，设与$x$轴、$y$轴方向相同的两个单位向量分别为$\vec{i},\vec{j}$，取$\{\vec{i},\vec{j}\}$作为基底. 对于平面内的任意一个向量$\vec{a}$，由平面向量的基本定理可知，有且只有一对实数$x,y$，使得$\vec{a}=x\vec{i}+y\vec{j}$，我们把有序数对$(x,y)$叫做向量$\vec{a}$的坐标，记作$$\vec{a}=(x,y)$$</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 在平面直角坐标系中，设与$x$轴、$y$轴方向相同的两个单位向量分别为$\vec{i},\vec{j}$，取$\{\vec{i},\vec{j}\}$作为基底. 对于平面内的任意一个向量$\vec{a}$，由平面向量的基本定理可知，有且只有一对实数$x,y$，使得$\vec{a}=x\vec{i}+y\vec{j}$，我们把有序数对$(x,y)$叫做向量$\vec{a}$的坐标，记作$$\vec{a}=(x,y)$$</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>其中，$x$叫做$\vec{a}$在$x$轴上坐标，$y$叫做$\vec{a}$在$y$轴上坐标，上式叫做$\vec{a}$的坐标表示.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>其中，$x$叫做$\vec{a}$在$x$轴上坐标，$y$叫做$\vec{a}$在$y$轴上坐标，上式叫做$\vec{a}$的坐标表示.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* 在直角坐标平面内，以$O$为起点的向量$\overrightarrow{OA}$的坐标就是终点$A$的坐标.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==例题==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==例题==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==练习==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==练习==</div></td></tr>
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2024-04-18T03:48:07Z
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[6.3 平面向量基本定理及坐标表示]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[6.3 平面向量基本定理及坐标表示]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==知识要点==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==知识要点==</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* 在平面直角坐标系中，设与$x$轴、$y$轴方向相同的两个单位向量分别为$\vec{i},\vec{j}$，取$\{\vec{i},\vec{j}\}$作为基底. 对于平面内的任意一个向量$\vec{a}$，由平面向量的基本定理可知，有且只有一对实数$x,y$，使得$\vec{a}=x\vec{i}+y\vec{j}$，我们把有序数对$(x,y)$叫做向量$\vec{a}$的坐标，记作$$\vec{a}=(x,y)$$</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">其中，$x$叫做$\vec{a}$在$x$轴上坐标，$y$叫做$\vec{a}$在$y$轴上坐标，上式叫做$\vec{a}$的坐标表示.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==例题==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==例题==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==练习==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==练习==</div></td></tr>
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Admin：创建页面，内容为“6.3 平面向量基本定理及坐标表示 ==知识要点== ==例题== ==练习==”
2024-04-18T03:21:06Z
<p>创建页面，内容为“<a href="/index.php/6.3_%E5%B9%B3%E9%9D%A2%E5%90%91%E9%87%8F%E5%9F%BA%E6%9C%AC%E5%AE%9A%E7%90%86%E5%8F%8A%E5%9D%90%E6%A0%87%E8%A1%A8%E7%A4%BA" title="6.3 平面向量基本定理及坐标表示">6.3 平面向量基本定理及坐标表示</a> ==知识要点== ==例题== ==练习==”</p>
<p><b>新页面</b></p><div>[[6.3 平面向量基本定理及坐标表示]]<br />
==知识要点==<br />
==例题==<br />
==练习==</div>
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