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Let a,b,c be in A.P and x,y,z be in G.P....

Let a,b,c be in A.P and x,y,z be in G.P.. Then the points `(a,x),(b,y)` and `(c,z)` will be collinear if

A

`x^2=y`

B

`x=y=z`

C

`y^2=z`

D

`x=z^2`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that a,b,c are in A.P.
`rArra-b=b-c`
Now, `(a,x),(b,y)and (c,z)` are collinear.
`rArr(x-y)/(a-b)=(y-z)/(b-c)`
`rArr (x-y)/(y-z)=(a-b)/(b-c)=1`
`rArrx-y=y-z`
So, x,y,z are in A.P.
Thus x,y,z are in A.P and also in G.P.
`therefore x=y=z`.
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