Question

已知非零向量a.b满足a的模=根号7+1,b的模根号7-1,且/a-b/=4,求/a+b/

Answer 1

(a-b)^2=|a|^2-2*a*b+|b|^2=16---->2*|a|*|b|=|a|^2+|b|^2-16

|a+b|=√(a+b)^2=√(|a|^2+2*|a|*|b|+|b|^2)=√[2*(|a|^2+|b|^2)-16]=4