Question

If m 1 m 2 =-1 then the curves are set to be​

Answer 1

This is actually much easier to understand if you look at it with the appropriate concepts for higher-dimensional geometry. Let me quote one of my earlier answers on a related topic for the relevant explanation:

I need a little bit of vector geometry to describe what's going on here. A vector is a list of coordinates  x⃗ =(x1,x2,xn) , and given two vectors  x⃗ =(x1,x2,,xn)  and  y⃗ =(y1,y2,,yn)  of equal length, we can define something called the dot product by  x⃗ ⋅y⃗ =x1y1+x2y+xnyn . The key thing to know about dot products is that two vectors are perpendicular if and only if their dot product is equal to zero.