How can I find the mirror plane that maps the plane $ax+by+c = 0$ to $a'x+b'y+c' = 0$? My approach involves finding the normal vector of the mirror plane. I believe that if $(a, b, c)$ and $(a', b', c')$ point towards the mirror, then the vector $(a, b, c) - (a', b', c')$ should be parallel to the normal vector of the mirror plane.
2026-03-26 01:03:27.1774487007
Finding the Mirror Plane Mapping One Plane to Another and Understanding the Relationship between Normal Vectors
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HINT…if the normals to the planes are $\underline{n}$ and $\underline{n}’$ then $\underline{n}-\underline{n}’$ will only be parallel to the normal of the mirror plane if these vectors have the same magnitude. Therefore they will both need to be normalised (i.e. write down the unit vector in each case), then subtract them. Bear in mind that there will be two possible mirror planes. Can you see how to find the other possible normal?