设向量a和b,坐标表示分别为(x1,y1)和(x2,y2),当(a-2b)⊥a,(x1-2x2)x1+(y1-2y2)y1=0,(x1)²-2x1x2+(y1)²-2y1y2=0,当(b-2a)⊥b,(x2-2x1)x2+(y2-2y1)y2=0,(x2)²-2x1x2+(y2)²-2y1y2=0,由上式得:(x1)²+(y1)²=(x2)²+(y2)²,2x1x2+2y1y2=(x1)²+(y1)²=(x2)²+(y2)²,向量公式:a●b=|a|●|b|cos(a,b),a●b=[(x1)²+(y1)²]/2,|a|●|b|=(x1)²+(y1)²,cos(a,b)=1/2,向量a和b夹角60°.
,(x1-2x2)x1+(y1-2y2)y1=0,是怎么回事?
向量a⊥b,a●b=0,坐标表示xx'+yy'=0.