7. \u70b9\u79ef\u4e0e\u5bf9\u5076\u6027
<\/p>\n\n\n\n
\u4e24\u4e2a\u7ef4\u6570\u76f8\u540c\u7684\u5411\u91cf $\\vec{v}\\cdot\\vec{w}$\uff0c\u70b9\u79ef\u8868\u793a\u5bf9\u5e94\u76f8\u4e58\u540e\u76f8\u52a0\u3002\u5982\uff1a<\/p>\n\n\n\n
$\\begin{bmatrix}
3 \\\\
5 \\\\
1
\\end{bmatrix} \\cdot \\begin{bmatrix}
2 \\\\
1 \\\\
1
\\end{bmatrix} = 3 \\times 2 + 5 \\times 1 + 1 \\times 1 = 12$<\/p>\n\n\n\n
\u5b83\u7684\u51e0\u4f55\u89e3\u91ca\u4e3a\uff0c\u4e00\u4e2a\u5411\u91cf\u5728\u53e6\u4e00\u4e2a\u5411\u91cf\u4e0a\u7684\u6295\u5f71\u7684\u957f\u5ea6\u4e0e\u53e6\u4e00\u4e2a\u5411\u91cf\u7684\u957f\u5ea6\u7684\u4e58\u79ef\u3002\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u5782\u76f4\uff0c\u5219\u70b9\u79ef\u4e3a $0$ . \u5982\u679c\u4e24\u4e2a\u5411\u91cf\u7684\u5939\u89d2\u5927\u4e8e $90\u00b0$\uff0c\u5219\u70b9\u79ef\u4e3a\u8d1f\u6570\u3002<\/p>\n\n\n\n
\u70b9\u79ef\u4e2d\u4e24\u4e2a\u5411\u91cf\u7684\u987a\u5e8f\u65e0\u5173\u3002<\/p>\n\n\n\n
$ 1 \\times 2 $ \u77e9\u9635\u548c\u5411\u91cf\u7684\u8054\u7cfb\uff1a<\/p>\n\n\n\n
\u5047\u8bbe\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u6709\u4e00\u4e2a\u5355\u4f4d\u957f\u5ea6\u7684\u5411\u91cf $\\vec{u}[u_x, u_y]^T$ (\u8be5\u5411\u91cf\u6709\u4e00\u4e2a\u81ea\u5df1\u7684\u65b9\u5411\uff09, \u6211\u4eec\u53ef\u4ee5\u6cbf\u7740\u8fd9\u4e2a\u65b9\u5411\u5efa\u7acb\u4e00\u4e2a\u5750\u6807\u8f74\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e2a\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u7684\u5411\u91cf\u6295\u5f71\u5230\u8fd9\u4e2a\u5750\u6807\u8f74\u4e0a\uff0c\u8fd9\u79cd\u4e8c\u7ef4\u5230\u4e00\u7ef4\u7684\u53d8\u6362\u663e\u7136\u5bf9\u5e94\u4e86\u4e00\u4e2a $ 1 \\times 2 $ \u7684\u77e9\u9635 $\\boldsymbol{A}=[A_x, A_y]$ .<\/p>\n\n\n\n
\u4e3a\u4e86\u786e\u5b9a $A_x$ \u548c $A_y$ \uff0c\u56de\u5fc6\u4e4b\u524d\u7684\u5185\u5bb9\u53ef\u77e5\uff0c$A_x$ \u662f\u4e8c\u7ef4\u7a7a\u95f4\u4e2d $\\hat{i}$ \u53d8\u6362\u540e\u7684\u65b0\u5750\u6807\uff0c\u4e5f\u5c31\u662f $\\hat{i}$ \u5728 $\\hat{u}$ \u65b9\u5411\u4e0a\u7684\u6295\u5f71\uff08\u548c\u65b9\u5411\uff09\uff1b\u800c $A_y$ \u662f\u4e8c\u7ef4\u7a7a\u95f4\u4e2d $\\hat{j}$ \u53d8\u6362\u540e\u7684\u65b0\u5750\u6807\uff0c\u4e5f\u5c31\u662f $\\hat{j}$ \u5728 $\\hat{u}$ \u65b9\u5411\u4e0a\u7684\u6295\u5f71\uff08\u548c\u65b9\u5411\uff09\u3002<\/p>\n\n\n\n
\u6839\u636e\u5bf9\u79f0\u6027\uff0c$\\hat{i}$ \u5728 $\\hat{u}$ \u65b9\u5411\u4e0a\u7684\u6295\u5f71\u7684\u957f\u5ea6\u5e94\u8be5\u4e0e $\\hat{u}$ \u5728 $\\hat{i}$ \u65b9\u5411\u4e0a\u6295\u5f71\u7684\u957f\u5ea6\u4e00\u81f4\uff08$\\hat{i}$ \u548c $\\hat{u}$ \u5f62\u6210\u7684\u5939\u89d2\u7684\u89d2\u5e73\u5206\u7ebf\u4e3a\u5bf9\u79f0\u8f74\uff09\u56e0\u6b64\uff0c$A_x$ \uff0c\u4e5f\u5c31\u662f$\\hat{i}$ \u6295\u5f71\u7684\u957f\u5ea6\u5e94\u8be5\u7b49\u4e8e $\\hat{u}$ \u5728 $\\hat{i}$ \u65b9\u5411\u4e0a\u7684\u6295\u5f71\u957f\u5ea6\uff0c\u4e5f\u5c31\u662f $\\hat{u}$ \u7684\u6a2a\u5750\u6807 $u_x$ . \u540c\u7406\u53ef\u5f97 $A_y=u_y$ .<\/p>\n\n\n\n
\u56e0\u6b64\uff0c\u8fd9\u79cd\u53d8\u6362\u5bf9\u5e94\u7684\u77e9\u9635 $\\boldsymbol{A}=[u_x, u_y]$ . \u800c\u66f4\u5de7\u5999\u7684\u662f\uff0c\u8fd9\u79cd\u53d8\u6362\u5bf9\u4efb\u610f\u4e00\u4e2a\u5411\u91cf${x \\brack y}$ \u7684\u4f5c\u7528\u7ed3\u679c $
[u_x, u_y] { x \\brack y } $ \u6070\u597d\u4e0e\u5411\u91cf $\\vec{u}$ \u4e0e\u8be5\u5411\u91cf\u7684\u70b9\u79ef\u7ed3\u679c\u4e00\u81f4\u3002<\/p>\n\n\n\n
\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u70b9\u79ef\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e00\u4e2a\u5411\u91cf\u4e0e\u53e6\u4e00\u4e2a\u5411\u91cf\u6295\u5f71\u7684\u4e58\u79ef\u3002<\/p>\n\n\n\n
\u5bf9\u4e8e\u975e\u5355\u4f4d\u957f\u5ea6\u7684\u5411\u91cf\uff0c\u7531\u4e8e\u6295\u5f71\u7684\u7ebf\u6027\u5173\u7cfb\uff0c\u6211\u4eec\u53ef\u4ee5\u7406\u89e3\u4e3a\u5148\u628a\u53e6\u4e00\u4e2a\u5411\u91cf\u6295\u5f71\uff0c\u518d\u7f29\u653e\uff08\u4e3a\u8fd9\u4e2a\u975e\u5355\u4f4d\u957f\u5ea6\u5411\u91cf\u7684\u957f\u5ea6\uff09\u3002<\/p>\n\n\n\n
\u4e00\u4e2a $ 1 \\times 2 $ \u7684\u77e9\u9635\uff08\u4e8c\u7ef4\u5230\u4e00\u7ef4\u7684\u53d8\u6362\uff09\u5fc5\u5b9a\u4e0e\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u5411\u91cf\u5bf9\u5e94\uff08\u5bf9\u5076\u6027\uff09<\/p>\n\n\n\n \n\n\n\n \n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[7,13],"tags":[],"class_list":["post-507","post","type-post","status-publish","format-standard","hentry","category-7","category-13"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.vincedeck.top\/index.php?rest_route=\/wp\/v2\/posts\/507","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vincedeck.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vincedeck.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vincedeck.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vincedeck.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=507"}],"version-history":[{"count":3,"href":"https:\/\/www.vincedeck.top\/index.php?rest_route=\/wp\/v2\/posts\/507\/revisions"}],"predecessor-version":[{"id":510,"href":"https:\/\/www.vincedeck.top\/index.php?rest_route=\/wp\/v2\/posts\/507\/revisions\/510"}],"wp:attachment":[{"href":"https:\/\/www.vincedeck.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=507"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vincedeck.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=507"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vincedeck.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=507"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}