So I have a scalar equation of 3x-2y+5z-2=0. Apparently a point on this plane is (0, 0, 2/5) according to the answers. How can you determine this given only the equation? Thanks.
Are you asking how you can verify that a point is on that plane? That is easy: Just plug in the values of x, y and z of the point into the equation above and see if it holds. In your case, you have x=0, y=0 and z=2/5.
Or, if you are only concerned with finding a single point on the plane, choose whatever numbers you like for any two of x, y, and z, put them into the equation, and solve for the remaining variable. For example, putting x= 0, y= 0 into the equation $\displaystyle 3x+ 2y+ 5z- 2= 0$ gives $\displaystyle 5x- 2= 0$ so that $\displaystyle x= 2/5$. Or, if you put x= 0, z= 2/5 into the equation you get $\displaystyle 2y+ 2- 2= 0$ which reduces to $\displaystyle y= 0$.