羁绊6.52地图下载:设a=（cos x/2,sinx/2) b=(sin3x/2,sin3x/2) x∈[0, pai/2]

来源：百度文库编辑：高考问答时间：2024/04/30 20:48:12

设a=（cos x/2,sinx/2) b=(sin3x/2,sin3x/2) x∈[0, pai/2]
（1）若a‖b，求x的值.
（2）求|a+b|的取值范围.

解.（1）∵a‖b
∴cosx/2cos3x/2-sinx/2sin3x/2=0
即cos2x=0
∵x∈[0,π/2 ]
∴x=pai/4
(2)|a+b|^2 =|a|^2 +|b|^2 =2a•b=2+2sin2x
∵x∈[0,pai/2 ]
∴2x∈[0,π]
2+2sin2x∈[2,4]
∴|a+b|∈[sqr2 ,2]

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