  According to celebrated Hurwitz theorem, there exists four division algebras
consisting of R (real numbers), C (complex numbers), H (quaternions) and O
(octonions). Keeping in view the utility of octonion variable we have tried to
extend the three dimensional vector analysis to seven dimensional one. Starting
with the scalar and vector product in seven dimensions, we have redefined the
gradient, divergence and curl in seven dimension. It is shown that the identity
n(n-1)(n-3)(n-7)=0 is satisfied only for 0, 1, 3 and 7 dimensional vectors. We
have tried to write all the vector inequalities and formulas in terms of seven
dimensions and it is shown that same formulas loose their meaning in seven
dimensions due to non-associativity of octonions. The vector formulas are
retained only if we put certain restrictions on octonions and split octonions.
