高一向量(在线)

(a+3b)(7a-5b)=7a^2+16ab-15b^2=0
(a-4b)(7a-2b)=7a^2-30ab+8b^2=0
得b^2=2ab,a^2=2ab,a^2b^2=(2ab)^2,
|a||b|=2ab
cosa与b的夹角=(ab)/|a||b|=1/2
a与b的夹角60°

a+3b与7a-5b垂直 =>(a+eb)(7a-5b)=0 => 7a^2+16ab-15b^2=0①
a-4b与7a-2b垂直 =>(a-4b)(7a-2b)=0 => 7a^2-30ab+8b^2=0②
①-②得 46ab=23b^2 => 2|a|cosA=|b|③
15①+8②得161a^2=161b^2 =>|a|=|b|④
由③④ 2cosA=1 =>A=60°