P1(X1,y1),P2(x2,y2),O为原点,x1x2+y1y2=0,求△P1OP2中∠P1OP2大小
问题描述：
P1(X1,y1),P2(x2,y2),O为原点,x1x2+y1y2=0,求△P1OP2中∠P1OP2大小
答
OP1^2=X1^2+y1^2,OP2^2=X2^2+y^2,P1P2^2=(X1-X2)^2+(y1-y2)^2=x1^2-2x1x2+x2^2+y1^2-2y1y2+y2^2=x1^2+x2^2+y1^2+y2^2-2(x1x2+y1y2)=x1^+x2^2+y1^2+y2^2cos∠P1OP2=(OP1^2+OP2^2-P1P2^2)/(2OP1*OP2)=(x1^2+y1^2+x2^2+...