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I am trying to define a coordinate system for some data in three-space. I have a normal vector v = (a,b,c) = (135, 62, 1005) that passes through the origin (0,0,0). And I am defining the plane to have this vector be the normal vector and to also contain the origin.

I dont know how to find the equation of such a plane.

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The plane $P:135x + 62y + 1005z = 0$ passed through the origin, and has $(135,62,1005)$ as its normal vector.

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