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in Three-dimensional geometry by (36.3k points)

A plane π passes through the point (1, 1, 1) and is parallel to the vectors b = (1, 0, –1) and c = (–1, 1, 0). If π meets the axes in A, B and C, find the volume of the tetrahedron OABC.

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As the plane π parallel to b = (1, 0, –1) and c = (– 1, 1, 0) normal to the plane is given by 

∴ The equation of the plane ABC is

1.(x – 1) + 1.(y – 1) + 1.(z – 1) = 0 

x + y + z – 3 = 0

x + y + z = 3 

x/3 + y/3 + z/3 = 1.

This planes meets the axes in A(3, 0, 0), B(0, 3, 0), C(0, 0, 3).

Thus, volume of the tetrahedron OABC

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