Finding the distance between origin and a plane.

[Usernam]

The Attempt at a Solution

I could not figure out the first part, though i know that distance is λn, λ being any non-zero scalar. But i could not figure out the first question it self.

 

[HallsofIvy]

Well, what do you know about these things? Do you know, for example, that a vector perpendicular to the plane ax+ by+ cz= d is a multiple of <a, b, c>? Do you know that a line, through the origin, in the direction of <a, b, c> has parametric equations x= at, y= bt, z= ct? Where does the line x= at, y= bt, z= ct intersect the plane ax+ by+cz= d?

(Actually, the one thing you say you know, "that distance is λn, λ being any non-zero scalar", is not true, but I think it is a typo- you mean \lambda ||n||.)