已知向量a=(cos3X/2,sin3X/2）,向量b=（cosX/2,-sinX/2）,且0≤X≤60°

1.a*b=cos3x/2*cosx/2-sin3x/2*sinx/2
=cos2x
a+b=(cos3x/2+cosx/2,sin3x/2-sinx/2)
|a+b|^2=2+2(cos3x/2cox/2-sin3x/2sinx/2)
=2+2cos2x
=4cos^2 x
a*b/|a+b|=cos2x/2cosx
2.|ka+b|^2+|a-kb|^2=(k^2+1)(a^2+b^2)
=2k^2+2
所以|a-kb|^2=(k^2+1)/2
ab=(k^2+1)/4k=cos2x
所以总是存在k的