1.由題意不妨設(shè)點(diǎn)P坐標(biāo)為(a,a²-a),則點(diǎn)P到直線y=x-3即x-y-3=0的距離為：
d=|a-a²+a-3|/根號(hào)2
=|a²-2a+3|/根號(hào)2
=|(a-1)²+2|/根號(hào)2
所以可知當(dāng)a=1時(shí),點(diǎn)P到直線y=x-3即x-y-3=0的距離d取得最小值為d=2/根號(hào)2=根號(hào)2
此時(shí)對(duì)應(yīng)點(diǎn)P的坐標(biāo)為(1,0)
2.log3/2=log3-log2=b-a
3.
1
由題意：a+b=(sinx+sqrt(3)cosx,-3/2),(a+b) dot a=(sinx+sqrt(3)cosx,-3/2) dot (sinx,-1)
=sinx(sinx+sqrt(3)cosx)+3/2=sinx^2+sqrt(3)sinxcosx+3/2=(1-cos2x)/2+sqrt(3)sin2x/2+3/2
所以：f(x)=(a+b) dot a-2=sqrt(3)sin2x/2-cos2x/2=sin(2x-π/6),所以f(x)的最小正周期：π
2
f(A)=sin(2A-π/6)=1,因A是銳角,故：-π/6