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Homework Help: Equation of normal

  1. Apr 19, 2009 #1
    Write equation of normal from point [tex]M(2,3,1)[/tex] into line:[tex]l: \frac{x+1}{2}=\frac{y-0}{-1}=\frac{z-2}{3}[/tex].

    I just have no idea about this problem. Any hint?

    Thank you.
  2. jcsd
  3. Apr 19, 2009 #2


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    What is the relationship between the line and the normal?
  4. Apr 19, 2009 #3
    Calculate the plane normal to the given line and that passes through 2,3,1

    Then calculate the point where the given line and the plane intersect.

    This point will enable you, together with the (2,3,1), to calculate the direction of the normal to the given line

  5. Apr 19, 2009 #4
    Let me understand this. I have to create a plane which passes through that point. Another point is point of intersection. But to find that point i must have a direction vector of that plane and I don't have so can you help me with point of intersection. How can i find it?

    So, when I have that point I have to create a vector which passes through point (2,3,1) and point of intesection and cross product of vector direction of line and vector I created will create a normal vector of plane. Am I right?

    Thank you.
    Last edited: Apr 19, 2009
  6. Apr 19, 2009 #5
    Let's take this one step at the time :

    First you need to find a plane that contains the point (2,3,1) and that is normal to the given line (your first equation).

    Let's start with that.

    Do you know how to do this ?

  7. Apr 20, 2009 #6
    No, can you help me with this and line of intersection?

    Thank you.
  8. Apr 20, 2009 #7
    let's say that the plane has equatiuon ux+vy+wz+t=0 where (u,v,w) is the normal vector of the plane and t is a constant. We need to find u,v,w and t.

    A) find u,v,w
    B) find t

    For A) i say that (u,v,w) denotes the same direction vector as the line.
    Do you know why and if so, what's the direction vector of the line ?

    If you have u,v,w then you can use the fact that (2,3,1) lies on the plane to find t

  9. Apr 20, 2009 #8
    So the normal vector has the same direction as line. So how to find that vector and t?
  10. Apr 21, 2009 #9
    Well, you know the normal vector (u,v,w) and you know one point on the plane

    Substitute these two variables in the ux+vy+wz+t=0 and solve for t

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