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Find a Cartesian equation of the plane parallel to a given vector and containing the intersection of two given planes

Find a Cartesian equation for the plane which is parallel to the vector 3 \mathbf{i} - \mathbf{j} + 2 \mathbf{k} and which contains every point on the line of intersection of the planes

    \[ x + y = 3, \qquad 2y + 3z = 4. \]


Incomplete.

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