看板 Math 關於我們 聯絡資訊
※ 引述《windowlove (回歸大海的笨魚)》之銘言: : 解到一半卡住 請版上各位幫個忙 : http://i.imgur.com/no5WErG.jpg
: 第六題 感謝了 : ----- : Sent from JPTT on my Sony F8332. a^表示a向量,|a^| = a = |b^| a, b之夾角 = 2k a^ + b^ = 2acos(k) a^ - b^ = 2asin(k) 2a[cosk - sink] = sqrt(2)a => sqrt(2)cos(Pi/4 + k) = 1/sqrt(2) => cos(k + Pi/4) = 1/2 => k = 15 a, b之間的夾角為30度 另解 |a^ + b^|^2 + |a^ - b^|^2 - 2|a^ + b^||a^ - b^| = 2a^2 => 2a^2 + 2b^2 - 2|a^ + b^||a^ - b^| = 2a^2 => b^4 = [a^2 + b^2 + 2abcos(2k)][a^2 + b^2 - 2abcos(2k)] => 0 = a^4 + 2(ab)^2 - 4[abcos(2k)]^2 = a^4 + 2(ab)^2 [1 - 2(cos(2k))^2] => cos(2k) = sqrt[a^2[a^2 + 2b^2]/(2ab)^2] = sqrt[3/4] => a, b之間的夾角為30度 -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 111.241.151.148 ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1510591658.A.2C3.html