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Math Help - Vector equation of line perpendicular to plane

  1. #1
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    Question Vector equation of line perpendicular to plane

    Consider three points A,B,C with coordinates (2,2,3) (1,1,0) and (1,0,1) respectively. Find a vector equation of the line through point A that is perpendicular to the plane that passes through all three points A,B,C. [Hint: Use point-normal equation]

    I am completely lost; the point normal equation bit throws me off the most.

    Point normal equation: A(x-x0) + B(y-y0) + C(z-z0) = 0
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  2. #2
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    Quote Originally Posted by axdv View Post
    Consider three points A,B,C with coordinates (2,2,3) (1,1,0) and (1,0,1) respectively. Find a vector equation of the line through point A that is perpendicular to the plane that passes through all three points A,B,C. [Hint: Use point-normal equation]

    I am completely lost; the point normal equation bit throws me off the most.

    Point normal equation: A(x-x0) + B(y-y0) + C(z-z0) = 0
    I don't understand that hint. the "point normal equation" is the equation of a plane and you want to find a line, not a plane.

    Instead, use the fact that the vector equation of a line through (x_0, y_0, z_0) and in the direction of vector A\vec{i}+ B\vec{j}+ C\vec{k} is \vec{r}(t)= (At+ x_0)\vec{i}+ (Bt+ y_0)\vec{j}+ (Ct+ z_0)\vec{k}.
    You already know that x_0= 2, y_0= 2, z_0= 3 so you just need to find a vector perpendicular to the plane. And you can do that by taking the cross product of the vectors (2- 1)\vec{i}+ (2- 1)\vec{j}+ (3- 0)\vec{k} (from B to A) and (1- 1)\vec{i}+ (0- 1)\vec{j}+ (1- 0)\vec{k} (from B to C).

    By the way, this is a "Calculus" problem. It doesn't belong in "Linear and Abstract Algebra".
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  3. #3
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    Thumbs up

    Thanks for the help
    And sorry about posting in the wrong place, I have difficulty telling different topics of maths appart.
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  4. #4
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    Im confused

    Can someone please explain that to me. Im a little lost.
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  5. #5
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    Quote Originally Posted by Surreptitous_Smiles View Post
    Can someone please explain that to me. Im a little lost.
    Explain what to you?
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