I have points in $n$-dimensions.
I want to find the points which lie on one side of the plane and other lies on the second side and i'm trying to do this with the help of dot-product.
Suppose i have $A = [x_1,x_2,...x_n]$ and $B = [x_1^{\prime},x_2^{\prime}.....x_n^{\prime}]$ and i want to find the sign of the point(which is given by $B$) .
I take the dot-product with $A$ and find out on which side of the plane($A$) does this point lie.
The values in $A$ are between $[-1 ,1]$ and values in $B$ are between $[0,50,000]$, so do i have to normalize $B$ so that both are on same scale or is there any disadvantage of not normalizing $B$?
Don't normalize. It is not quite clear what is the plane you are asking about, though.
You may find this answer helpful: https://stackoverflow.com/a/15691064/7566419