MATLAB: Matrix multiplication with different dimension

I need to perform a matrix multiplication with different dimensions, let

 A*B=C;

where the dimension of A is 700*5 and the dimension of C should be 1*5, what will be the dimension of B?? Is this possible??

No. However it would be possible if it were B*A = C instead, in which case B would have to be 1 x 700

Not sure if this is the operation you really want from your description:

a = 6x7 matrix
b = 7x3 matrix
c = a * b;  % 6x3 matrix

To do matrix multiplication the inner dimensions must agree. Both of your matrices are 1x5 vectors. You can do either of the following:

A' * B (results in a 5x5 matrix)

A * B' (results in a 1x1 scalar)