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Grade: 12
        

 A variable plane at a distance of 1 unit from the origin cuts the coordinate axis at A,B and C . If the centroid (x,y,z) of triangle ABC satisfy the relation 1/x2 + 1/y2 + 1/z2 = k, then the value of k is


A)3


B)1


C)1/3


D)9

10 years ago

Answers : (1)

Ramesh V
70 Points
							

let the plane be x/a + y/b + z/c = 1  with x,y,z intercepts as a, b, c respectively.

given perpendicular distance is 1, so

1/a2 +1/b2 + 1/c2 = 1

centroid is (a/3, b/3, c/3)

so 9/a2 +9/b2 +9/c2 = k   which implies k=9 on comparision

option D

--

regards

Ramesh

10 years ago
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