Equation of line formed by intersection if two planes.
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Write equations of a line as intersections of two planes Example: Write the parametric and sysmetric equations of the line of intersection of the planes 2x — y + z = 5 and + y —z = 1. Solution: The planes have normal vectors a = (2, —1, 1) and b = (1, 1, —1), respectively. Let L denote the line of intersection. Then v = a >< b = (1 — (0, 3, 3) is parallel to L. We only need to find a point P on L. To find P, solved the system of equations of the planes: '2x — y + z = 5 and x + y — z —1. We consider P to be the point of L on the plane z = 0. Thus substitute z — 0 in the ssytem above to get '2x — y = 5 and + y = 1 x = 2, y Hence we get P (2, —1, 0), and so the equations of the line are = — I + 3 t and x — 2 , + I
Discussion
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