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
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![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](/uploads/image/z/8571507-51-7.jpg?t=%E5%9C%A8%E5%B9%B3%E9%9D%A2%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E7%B3%BB%E4%B8%AD%2C%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8FOA%3D%28cos80%C2%B0%2Csin80%C2%B0%29%E5%90%91%E9%87%8FOB%3D%28cos20%C2%B0%2Csin20%C2%B0%29+%E6%B1%82%E7%BB%9D%E5%AF%B9%E5%80%BC%E5%90%91%E9%87%8FAB+.%E8%8B%A5AB%E4%B8%AD%E7%82%B9%E6%98%AFC%2C%E6%B1%82%E5%90%91%E9%87%8FOC)
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 )