已知向量a=(cos2π/3,sin2π/3),向量OA =a-b,向量OB=a+b

由直角得：OA·OB=(a-b)(a+b)=a²-b²=0 ∴‖a‖=‖b‖
由等腰得：‖OA‖=‖OB‖ 即 ‖a-b‖=‖a+b‖ ∴√（a-b）²=√（a+b）²
∴ a²-2ab+b²=a²+2ab+b² ∴-2ab=2ab=0
又 S△AOB=1/2×OAOB=1/2×√（a-b）²√（a+b）²=1/2×√（a²-2ab+b²）√（a²+2ab+b²）=1/2×2a²=a²=（√cos²2π/3+sin²2π/3）²=1