已知a=(2sinx,根号3sinx),b=(cosx,2sinx),c=(2cosx,sinx)(1)求a乘b和|b-c|
问题描述:
已知a=(2sinx,根号3sinx),b=(cosx,2sinx),c=(2cosx,sinx)(1)求a乘b和|b-c|
答
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)]