P1(X1,y1),P2(x2,y2),O为原点,x1x2+y1y2=0,求△P1OP2中∠P1OP2大小

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+y2^2
cos∠P1OP2=(OP1^2+OP2^2-P1P2^2)/(2OP1*OP2)
=(x1^2+y1^2+x2^2+y2^2-x1^2-x2^2-y1^2-y2^2)/(2OP1*OP2)
=0
所以∠P1OP2=90度