The following question i am having problems with:
1) Find the equation of the plane normal to the vector 2i+j-3k
book's answer says or
2) Find the equation of the plane which passes through the points (1,6,1), (3,5,2) and (3,2,1)
1,6,1), B3,5,2) and C3,2,1)" alt="A1,6,1), B3,5,2) and C3,2,1)" />
At plane (1,6,1)
therefore equation is
however book's answer is
The first question sounds strange to me. All equations of the form
are equations for planes with as a normal vector, regardless of what is. Is there some extra information, like a point the plane must pass through?
Where did the expression come from? Was meant to be ?
As for question 2, notice that you have a slight disagreement with the book's answer. While you have , the book has (so notice the on the ).
Ah, I see.
You write that the equation of the plane is given by . You probably didn't mean this. This expression is the distance from the plane to the origin.
You are being told that this distance is 5, so that . You already have , , and :
So insert these pieces of information into the formula for the distance from the plane to the origin:
giving you the two required solutions.