已知a=（2sinx,根号3sinx）,b=（cosx,2sinx）,c=（2cosx,sinx）（1）求a乘b和|b-c|

a*b=2sinxcosx+（2根号3 ）sin^x
=sin2x+根号3-（根号3）cos2x
=2sin(2x-π/3)+根号3
(|b-c|)^=b^+c^+2bc
=cos^x+4sin^x+4cos^x+sin^x+4cos^x+4sin^x
=9cos^x+9sin^x
=(9根号2)sin(x+π/4)
∴|b-c|=根号[(9根号2)sin(x+π/4)]