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If a plane meets the coordinates axes at A, Band C, in such a way that the centroid of `Delta ABC` is at the point `(1,2,3)`, the equation of the plane is

A

`x+(y)/(2)+(z)/(2)=1`

B

`(x)/(3)+(y)/(6)+(z)/(9)=1`

C

`x+2y+3z=1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let the plane meets the coordinate axes at A,B and C.
Let OA=a, OB=b and OC = c

Then, the centroid of `DeltaABC` is `((a)/(3),(b)/(3),(c)/(3))=(1,2,3)` [given]
`rArr" "a=3,b=6,c=9`
Then, the equation of plane, meet the coordinate axes is
`(x)/(a)+(y)/(b)+(z)/(c)=1`
`:." "(x)/(3)+(y)/(6)+(z)/(9)=1`
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