在平面直角坐标系中,已知向量OA=(cos80°,sin80°)向量OB=(cos20°,sin20°) 求绝对值向量AB .若AB中点是C,求向量OC

在平面直角坐标系中,已知向量OA=(cos80°,sin80°)向量OB=(cos20°,sin20°) 求绝对值向量AB .若AB中点是C,求向量OC
在平面直角坐标系中,已知向量OA=(cos80°,sin80°)向量OB=(cos20°,sin20°) 求绝对值向量AB .若AB中点是C,求向量OC

在平面直角坐标系中,已知向量OA=(cos80°,sin80°)向量OB=(cos20°,sin20°) 求绝对值向量AB .若AB中点是C,求向量OC
AB=OB-OA
=(cos20,sin20)-(cos80,sin80)
=(cos20-cos80,sin20-sin80)
=(2sin50sin30,-2cos50sin30)
=(sin50,-cos50)
|AB|=sqrt [sin²50+(-cos50)²]
=sqrt (sin²50+cos²50)
=sqrt 1
=1
OC=(OA+OB)/2
=[(cos80,sin80)+(cos20,sin20)]/2
=(cos80+cos20,sin80+sin20)/2
=(2cos50cos30,2sin50cos30)/2
=( (sqrt 3)/2*cos50,(sqrt 3)/2*sin50 )