Find a vector of magnitude 26 units normal to the plane 12x – 3y + 4z = 1.

The vector equation of the plane 12x – 3y + 4z = 1 can be written as

The normal to this plane is

Its magnitude is

The unit vector becomes

Now a vector normal to the plane with the magnitude 26 will be

Therefore, a vector of magnitude 26 units normal to the plane 12x – 3y + 4z = 1 is