Question

已知向量a,b为非零向量,且|a+b|=|a-b|.1求证a垂直b；2若|a|=2,|b|=1,求a-2b与b的夹角 θ

Answer 1

|a+b|=|a-b| |a+b|^2=|a-b|^2 a*b=0 ∴ a垂直b

|a-2b|^2=a^2-4ab+4b^2=4-4*0+4=8

｜a-2b｜=√8

cosa=(a-2b)*b/|b||a-2b|=-√2/2

a=135