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Math Help - normal vector

  1. #1
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    normal vector

    If  n is a normal vector of a plane, then it is perp. to every vector on the plane right? Let  \vec{r}, \vec{r_0}, \vec{r_1} -\vec<br />
{r_0} be vectors on the plane.


    Then  n \cdot (\vec{r}-\vec{r_0}) = 0 .


    Then shouldnt  n \cdot \vec{r_0} = n \cdot \vec{r_1} = 0 ?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by shilz222 View Post
    If  n is a normal vector of a plane, then it is perp. to every vector on the plane right? Let  \vec{r}, \vec{r_0}, \vec{r_1} -\vec<br />
{r_0} be vectors on the plane.


    Then  n \cdot (\vec{r}-\vec{r_0}) = 0 .


    Then shouldnt  n \cdot \vec{r_0} = n \cdot \vec{r_1} = 0 ?
    when we refer to  n \cdot (\vec{r}-\vec{r_0}) = 0 , we are referring to the (vector) equation of a plane. in this "construct", r - r_0 is a vector in the plane, but r and r_0 are actually vectors beginning at the origin whose terminal points are points in the plane, so individually, they are not necessarily perpendicular to the normal vector
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