问题
选择题
已知△ABC为等边三角形，AB=2．设点P，Q满足
|
答案
∵
=λAP
，AB
=(1-λ)AQ
，λ∈RAC
∴
=BQ
+BA
=AQ
+(1-λ)BA
，AC
=CP
+CA
=AP
+λCA AB
∵△ABC为等边三角形，AB=2
∴
•BQ
=CP
•BA
+λCA
•BA
+（1-λ）AB
•AC
+λ(1-λ)CA
•AC AB
=2×2×cos60°+λ×2×2×cos180°+（1-λ）×2×2×cos180°+λ（1-λ）×2×2×cos60°
=2-4λ+4λ-4+2λ-2λ2，
=-2λ2+2λ-2
∵
•BQ
=-CP 3 2
∴4λ2-4λ+1=0
∴（2λ-1）2=0
∴λ=1 2
故选A
