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in Three-dimensional geometry by (52.5k points)

A variable plane passes through a fixed point (3, 2, 1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz-plane through A, a second plane is drawn parallel zx-plane through B and a third plane is drawn parallel to xy-plane through C. Then, the locus of the point of intersection of these three planes, is

(A) x/3 + y/2 + z/1 = 1

(B) x + y + z = 6

(C) 1/x + 1/y + 1/z = 11/6

(D) 3/x + 2/y + 1/z = 1

1 Answer

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Answer is (D) 3/x + 2/y + 1/z = 6

Equation of plane is given as

x/a + y/b + z/c = 1

Therefore, the equation of plane passing through (3, 2, 1) is

3/a + 2/b + 1/c = 1

Points on axes are A(a, 0, 0), B(0, b, 0) and C(0, 0, c). 

Therefore, the locus of intersection point of plane through point A, B and C. Parallel to yz-, zx- and xy- plane, respectively, is

3/x + 2/y + 1/c = 1

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