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+1 vote
10.9k views
in JEE by (3.3k points)
edited by

A variable plane x/a+y/b+z/c=1 at a unit distance from origin cuts the coordinate axes at A,B and C. centroid(x,y,z) satisfies the equation 1/x2+1/y2+1/z2=K.the value of K?

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1 Answer

+1 vote
by (20.4k 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     

so 9(1/a2 +1/b2 + 1/c2) = k  

k = 9

by (3.3k points)
thanks a lot

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