I apologize if this isnt in the right place, my actual subject is mechanics. I've know how to do some of this question but stuck on other parts.
Consider the set of points (x,y,z)∈R3 lying in the plane x+y+z=1.
(i) Write the equation for this plane in the vector form
r · nˆ = d,
where d ∈ R is a constant and nˆ is a unit vector.
(ii) What is the distance of this plane from the origin (0, 0, 0)?
(iii) State the vector equation of the line that passes through the point(1, 2, 2) and is parallel to the vector nˆ .
(iv) Find the point where this line intersects the plane r · nˆ = d.
(v) Hence find the distance between the point (1,2,2) and the plane
x + y + z = 1.
For (i) I have the plane equation as r=a+tn^ where a is a point from (x,y,z) and t is a constant. But I'm confused over the form they want it in.