𝒂・𝒃 = |𝒂||𝒃|cos60° = 21/2
AP = (6𝒂 + 7𝒃)/13
|AP|² = (6𝒂 + 7𝒃)/13 ・ (6𝒂 + 7𝒃)/13
= (6𝒂 + 7𝒃)・(6𝒂 + 7𝒃)/13²
= (6²|𝒂|² + 2・6・7・𝒂・𝒃 + 7²|𝒃|²)/13²
=(6²・7² + 6・7・21 + 7²・3²)/13²
=3²(4・7² + 2・7² + 7²)/13²
=3²・7³/13²
|AP| = 21√7/13
わかりました!ありがとうございます!