Question

向量a=(1,1),向量b=(2,n),|a+b|=a·b,求n

Answer 1

|a|=√(1^2+1^2)=√2

|b|=√(2^2+n^2)=√(4+n^2)

|a+b|=a*b

两边同时平方得

|a+b|^2=a^2*b^2

a^2+b^2+2ab=2*(4+n^2)

2+4+n^2+2(2+n)=2*(4+n^2)

n^2-2n-2=0

n=(2+-2√3)/2=1+√3或1-√3