Given, a=2i+2j−k and b=αi+βj+2k ∴‌‌a+b=(2+α)i+(2+β)j+k and a−b=(2−α)i+(2−β)j−3k But it is given |a+b|=|a−b| ⇒√(2+α)2+(2+β)2+12 =√(2−α)2+(2−β)2+9 ⇒‌‌4+α2+4α+4+β2+4β+1 =4+α2−4α+4+β2−4β+9 ⇒‌‌8α+8β=8 ⇒‌‌α+β=1