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If centroid of the triangle with vertices `(3c+2,2,0) , (2c,-1,-1)` and `(c+2, 3c+1,c+3)` coincides with the centre of the sphere `x^2+y^2+z^2+5ax-4by-2cz=13` then (A) `c=1` (B) `c=2` (C) `c=3` (D) `c=0`

A

`c=1`

B

`c=2`

C

`c=3`

D

`c=0`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If the centroid of the triangle with vertices (3c+2,2,0),(2c,-1,-1)and(c+2,3c+1,c+3) lies in the plane z=c , then the coordinates of the centroid are:

    A
    `(-(2)/(3),-(1)/(3),(1)/(3))`
    B
    `((10)/(3),(5)/(3),1)`
    C
    `((4)/(3),(2)/(3),(2)/(3))`
    D
    `((2)/(3),(1)/(3),-(1)/(3))`

  • lf origin is centroid of triangle with vertices (a, 1 , 3), (- 2, b, -5) and (4, 7, c), then (a, b, c) equiv

    A
    (2, 2,8)
    B
    (- 2,8,2)
    C
    (- 2,-8,- 2)
    D
    (-2, -8,2)

  • If A(a,2,2),B(a,b,1) and C(1,2,-2) are the vertices of triangle ABC and G(2,1,c) is centroid, then values of a,b and c are

    A
    `a=(1)/(2),b=1,c=1`
    B
    `a=5/2,b=-1,c=1/3`
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    `a=-1,b=1,c=3/2`
    D
    `a=1/2,b=1/2,c-1`

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