If a variable plane in 3-D space moves in such a way that the sum of its reciprocal of intercepts on the x and y-axis exceeds, the reciprocal of its intercept on the z-axis by 2, then all such planes will pass through the point:

Answer 1

The plane with intercepts a,b,c is
x/a + y/b + z/c = 1
Now, you also have 1/a + 1/b = 1/c + 2
So express c in terms of a and b, and find the sum k = 1/a+1/b+1/c.

Now, it is easy to find proofs online that if 1/a + 1/b + 1/c = k, then the plane passes through (1/k, 1/k, 1/k)

Answer 2

Thank u
So answer will be (1/2,1/2,-1/2)

Answer 3

That's what I get.