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A variable plane which remains at q cons...

A variable plane which remains at q constant distance `3p` from the origin cut the coordinate axes at `A ,\ B ,\ Cdot` Show that the locus o the centroid of triangle `A B C` is `x^(-2)+y^(-2)+z^(-2)=p^(-2)dot`

A

`x^(-2) + y ^(-2) +z^(-2)=p^(-2)`

B

`x^(-2) + y ^(-2) +z^(-2)=16p^(-2)`

C

`x^(-2) + y ^(-2) +z^(-2)=p^(2)`

D

`x^(-2) + y ^(-2) +z^(-2)=9p^(2)`

Text Solution

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The correct Answer is:
B
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AAKASH INSTITUTE ENGLISH-THREE DIMENSIONAL GEOMETRY -ASSIGNMENT SECTION - B
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  5. The plane x / 2 + y / 3 + z / 4 = 1 cuts the co-ordinate axes in A, B,...

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  6. The position vectors of points A and B are hati - hatj + 3hatk and 3h...

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  7. The vector equation of the plane through the point (2, 1, -1) and pass...

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  8. Find the vector equation of line passing through the point (1,2,-4)...

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  9. The line x + 2y - z - 3 = 0 = x + 3y - 2 - 4 is parallel to

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  10. The shortest distance between the lines 2x + y + z - 1 = 0 = 3x + y + ...

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  13. The plane vecr cdot vecn = q will contain the line vecr = veca + lambd...

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  15. Find the length of the perpendicular from the point (1,2,3) to the ...

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  19. The coordinates of the point P on the line vecr=(hati+hatj+hatk)+lamda...

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  20. The projection of the line segment joining the Points (1, 2, 3) and ...

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