I did PCA on my data and projected the data on first two eigen vectors. After projection I see that the scatter plot of the data starts from [-1,-1]. My data is all positive. Is it correct for the data to be negative in the projected space.
Yes, it is, there is no reason why a component cannot have negative values.
Let's take this matrix:
[[1, 1],[0.5, 1]]
The eigenvectors have negative values:
[[ 0.81649658, -0.81649658], [ 0.57735027, 0.57735027]]