已知向量a=(cos3\2,sin3\2),b=(cosx/2,-sinx/2),且x∈[0,π/2],求 |a+b|,求a乘b.
问题描述:
已知向量a=(cos3\2,sin3\2),b=(cosx/2,-sinx/2),且x∈[0,π/2],求 |a+b|,求a乘b.
答
(1)a*b=cos3/2x*cosx/2-sin3/2x*sinx/2
=cos(3/2x+x/2)=cos2x
/a+b/^2
=(a+b)^2
=a^2+b^2+2a*b=2+2cos2x
=4cosx^2
又x∈{-π/3,π/4},cosx∈[1/2,1]
所以/a+b/=2cosx