Question

设向量a,b满足｜a｜=｜b｜=1, a.b=-1/2 ｜a+2b｜=? 求过程 详细点

麻烦顺便说下相关知识点

Answer 1

(|a+2b|)^2=a^2+4b^2+4ab (平方和公式)
=1+4-4×(1/2) [a^2=(|a|)^2，b^2=(|b|)^2]
=5-2
=3
∴|a+2b|=√3 这个也是a^2=(|a|)^2相关的知识点

Answer 2

|A+2B|=根号[(A+2B)*(A+2B)]
=根号[A*A+2A*B+2B*A+4B*B]
=根号[|A|^2+4A*B+4|B|^2]
=根号[1-2+4]
=根号3

追问

麻烦说下相关知识点行么？

Answer 3

|a+2b|^2=a^2+4a*b+4b^2=1+4*(-1/2)+4*1=3
所以, |a+2b|=根号3

Answer 4

|A+2B|=根号[(A+2B)*(A+2B)]
=根号[A*A+2A*B+2B*A+4B*B]
=根号[|A|^2+4A*B+4|B|^2]
=根号[1-2+4]
=根号3

Answer 5

这类问题要先平方在开方做：
|a+2b|^2=a^2+4a*b+4b^2=1+4*(-1/2)+4*1=3
所以, |a+2b|=根号3
类似的问题也一样这样做。

Answer 6

解：｜a+2b｜^2=(a+2b)^2
=a^2+4ab+4b^2
=1-2+4
=3
所以， ｜a+2b｜=根号3