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Math Help - Find equation of plane passing through a point, perpendicular to a line

  1. #1
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    Find equation of plane passing through a point, perpendicular to a line

    Good day,

    Here is my current problem:

    Find the equation of the plane that passes through the point (-2, 3, 4) and is perpendicular to the line passing through the points (4, -2, 5) and (0, 2, 4).

    My attempt

    Well, I need a vector, which I obtained from the two given points. I get: (-4, 4, -1).
    Now, from my understanding, the point on the plane is perpendicular to this point, so I can form the general equation with them:

    Equation of plane:
    (-4, 4, -1).(x + 2, y - 3, z - 4) = 0
    When simplifed to its general form, I get:
    -4x + 4y - z = 16

    I think that I'm doing it correctly, however, I also feel as though I should be using the cross product. Can anyone point me in the right direction?
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  2. #2
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    Re: Find equation of plane passing through a point, perpendicular to a line

    Quote Originally Posted by johnstobbart View Post
    Here is my current problem:
    Find the equation of the plane that passes through the point (-2, 3, 4) and is perpendicular to the line passing through the points (4, -2, 5) and (0, 2, 4).

    My attempt
    Well, I need a vector, which I obtained from the two given points. I get: (-4, 4, -1).
    Now, from my understanding, the point on the plane is perpendicular to this point, so I can form the general equation with them:
    Equation of plane:
    (-4, 4, -1).(x + 2, y - 3, z - 4) = 0
    When simplifed to its general form, I get:
    -4x + 4y - z = 16
    You are correct.
    Thanks from johnstobbart
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  3. #3
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    Re: Find equation of plane passing through a point, perpendicular to a line

    Quote Originally Posted by Plato View Post
    You are correct.
    Thank you very much for your help
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