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The plane $II_1$ has equation $ax+by+cz=0$ and the plane $II_2$ has Cartesian equation $ax+by+cz=d$. The two planes are parallel and$ II_1$ passes through the origin. Find a parametric vector equation for the position of the line which passes through the orgin and is perpendicular to both planes

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The line is perpendicular to both the planes, so it will be parallel to the normal vector of the planes. And it passes through the origin. The direction ratios will be a, b and c.