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Math Help - Directional Derivatives

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    Directional Derivatives

    Find equations of the tangent plane and normal line to the surface at the point (-8, 0, 0).
    Tangent Plane: (make the coefficient of z equal to 1).
    __________________________.
    Normal line: ____,____
    ____ ,_____ , .


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    Quote Originally Posted by jffyx View Post
    Find equations of the tangent plane and normal line to the surface at the point (-8, 0, 0).
    Tangent Plane: (make the coefficient of z equal to 1).
    __________________________.
    Normal line: ____,____
    ____ ,_____ , .


    Thanks!
    Take F(x,y,z) = xe^y \cos z - z

    the tangent plane is given by: F_x(-8, 0, 0)(x + 8) + F_y(-8, 0, 0)(y - 0) + F_z(-8, 0, 0)(z - 0) = 0

    the normal line is given by: \left< -8,0,0 \right> + t \left< \text{normal vector to the above plane} \right>
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    How do you find the normal vector to the plane?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jffyx View Post
    How do you find the normal vector to the plane?
    when a plane is written in the form: ax + by + cz + d = 0

    the normal vector is given by: \vec n = \left< a,b,c \right>

    remember, you want to write it in the form where c = 1
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