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Math Help - tangent plane help

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    tangent plane help

    Two surfaces are said to be orthogonal at a point P if the normals to their tangent planes are perpendicular at P. Show that the surfaces z= 1/2(x+y -1) and z=1/2(1- x-y) are orthogonal at all points of intersection.
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    Quote Originally Posted by dexza666 View Post
    Two surfaces are said to be orthogonal at a point P if the normals to their tangent planes are perpendicular at P. Show that the surfaces z= 1/2(x+y -1) and z=1/2(1- x-y) are orthogonal at all points of intersection.
    Here's an outline - details left for you.

    Get a normal to the tangent plane for each surface: A normal to a tangent plane is given by (z_x)i + (z_y)j - k.

    Find the curve of intersection of the two surfaces by solving x^2 + y^2 - 1 = 1 - x^2 - y^2: x^2 + y^2 = 1

    Take the dot product of the two normals and substitute x^2 + y^2 = 1 into the result. The resulting expression should simplify to zero.
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