Write down the equation of a plane with normal vector n = 2, 7, 1 that does not pass through the origin.

Try this:
1. Common equation for a plane is: ax+by+cz+d=0, where a,b,c,d - numbers. According to the conditions, the plane does not pass through the origin, it means that d≠0.
2. According to definition of a plane with equation ax+by+cz+d=0, vector n(a;b;c) - is normal vector.
3. Using n(2;7;1) and two previous issues: 2x+7y+1+d=0, where d=const.