You should not be requiring an exact zero for those dot products, since in most circumstances your computations will involve round-off errors. Provide a tolerance for a difference from zero in accordance with the amount of error which you would reasonably expect.
Remember, Matlab’s ‘double’ format has only 53 bits in its significand (mantissa) which is equivalent to about 16 decimal places. Do something like this:
abs(dot(Normal,P2fornormal))<tol & abs(dot(Normal,P3fornormal))<tol
where ‘tol’ is approximately a few ‘eps’ times the product of the magnitudes you expect for ‘Normal’ and ‘P2’ or ‘P3’, the quantity ‘eps’ being 2^(-53),
