Question

向量题目

已知OP=(3,-4),OP绕原点逆时针分别转90°，120°到OM，OR的位置，求点M，R的坐标
OM=(rcos(m+90),rsin(m+90))=(4,3)
OP=(rcos(m+120),rsin(m+120))=(-1.5+2√3，1.5√3+2)

Answer 1

设OP=(rcosm,rsinm),
则：rcosm=3, rsinm=-4
OM=(rcos(m-90),rsin(m-90))=(rsinm,-rcosm)=(-4,-3)
OR=(rcos(m-120),rsin(m-120))=(rcosm*cos120+rsinm*sin120,rsinm*cos120-rcosmsin120)
=(3*(-1/2)+(-4)*((根号3)/2, (-4)*(-1/2)-3*(根号3)/2)
=(-(3/2)-2*根号3, 2-(3/2)*根号3)
所以：
M的坐标(-4,-3)
R的坐标(-(3/2)-2*根号3, 2-(3/2)*根号3)