Question

已知向量a=(1,n) 向量b=(-1,n) 若2a＋b与b垂直 则n=?

详细过程!急！

Answer 1

2a＋b与b垂直
(2a+b)b=0
2ab+bb=0
2(-1+n^2)+1+n^2=0
3n^2=1
n=根号3分之1

追问

2(-1+n^2)+1+n^2=0
3n^2=1
什么意思

追答

2ab+bb=0
ab=(1,n)(-1,n)=n^2-1
bb=n^2+1
所以 2(n^2-1)+n^2+1=0
2n^2-2+n^2+1=0
3n^2=1