In a four-dimensional space where unit vectors along the axes are ` hat i , hat j , hat k` and `hat l`, and `vec a_1, vec a_2, vec a_3, vec a_4` are four non-zero vectors such that no vector can be expressed as a linear combination of others and `(lambda-1)( vec a_1- vec a_2)+mu( vec a_2+ vec a_3)+gamma( vec a_3+ vec a_4-2 vec a_2)+ vec a_3+delta vec a_4=0,` then