OP = aOA+bOB
OP.OA =(aOA+bOB).OA
|OP||OA|cos30度 = a|OA\^2 +b|OA||OB|cos30度
√3 = a+√3b/2 (1)
also
|OP|^2 =(aOA+bOB). (aOA+bOB)
= a^2|OA|^2+b^2|OB|^2 + 2abOA.OB
4 = a^2+b^2+ √3ab (2)
sub(1) into (2)
4 = ( √3 -√3b/2)^2 +b^2 + √3( √3 -√3b/2)b
= 3 + 3b^2/4 - 3b +b^2 + 3b - 3b^2/2
b^2-4 =0
b = 2 or -2
b=2 , a=0
b=-2, a=2√3
本文如未解决您的问题请添加抖音号:51dongshi(抖音搜索懂视),直接咨询即可。