设向量a、b满足|a|=|b|=1,且|3a-2b|=3,|3a+b|等于?

问题描述:

设向量a、b满足|a|=|b|=1,且|3a-2b|=3,|3a+b|等于?

|a|=|b|=1,则a^2 =1,b^2=1.
|3a-2b|=3,平方得:
9a^2-12a•b+4b^2=9,
9-12a•b+4=9,
a•b=1/3.
|3a+b|^2=9a^2+6a•b+b^2=9+2+1=12,
|3a+b|=2√3.