Plane equation of parallel vector (0,2, - 3) passing through point (- 1,2,0) (1,2, - 1) | Math enthusiast | Mathematical art

Plane equation of parallel vector (0,2, - 3) passing through point (- 1,2,0) (1,2, - 1)

It is known that a (- 1,2,0), B (1,2, - 1)
AB=（2,0,-1）
So we can know that the plane normal vector is perpendicular to AB and (0,2, - 3)
The normal vector is n (2,6,4), that is n (1,3,2)
The point P (x, y, z) on the plane satisfies AP ⊥ n,
So the plane equation is (x + 1) + 3 (Y-2) + 2Z = 0
That is, x + 3Y + 2Z = 5

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