Word Count : 441

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To find the distance of the origin \((0,0,0)\) from the plane passing through the three given points \((2,1,8)\), \((1,0,2)\), and \((-3,4,6)\), follow these steps: ### Step 1: Find the equation of the plane The general equation of a plane is: \[ Ax + By + Cz = D \] #### Step 1.1: Find the normal to the plane A normal vector to the plane can be found using the cross product of two vectors lying on the plane. Define two vectors using the given points: \[ \mathbf{v_1} = (1,0,2) - (2,1,8) = (-1, -1, -6) \] \[ \mathbf{v_2} = (-3,4,6) - (2,1,8) = (-5, 3, -2) \] The normal vector __________ ______ _________ ____ ___ _______ ______ ___ __________ ___ _______ ________.
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