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A variable plane is at a distance, k fro...

A variable plane is at a distance, k from the origin and meets the coordinates axis in A, B , C. Then, the locus of the centroid of `triangleABC` is

A

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

B

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

C

`(1)/(9)((1)/(x^2+(1)/(y^2)+(1)/(z^2)))=0`

D

`X+Y=0`

Text Solution

Verified by Experts

The correct Answer is:
(b,c)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (More Than One Correct Option Type Questions)
  1. Which of the following statements is/are correct?

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  2. Which of the following is/are correct about a tetrahedron?

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  3. A variable plane is at a distance, k from the origin and meets the coo...

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  4. Find the equation of the plane containing the line : (x+1)/1=(y-2)/2=(...

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  5. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve x^2+y^2=r...

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  6. A vector equally inclined to the vectors hat(i)-hat(j)+hat(k) and hat(...

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  7. Find the equations of the line through the point ( 1 , -2, -3) and par...

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  8. A plane passes through a fixed point (a, b, c) and direction ratios of...

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  9. Let A be vector parallel to line of intersection of planes P1 and P2. ...

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  10. Find the angle between the planes 2x+y+z-1=0 and 3x+y+2z-2=0,

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  11. Find the direction ratios of this plane 2x-3y+4z+2=0

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  12. A line segment has length 63 and direction ratios are 3,-2 and 6. The ...

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  13. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

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  14. The points A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices ...

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  15. The lines x=y=z meets the plane x+y+z=1 at the point P and the sphere ...

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  16. Evaluate int 4x^5 dx

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  17. Consider the planes 2x+y+z+4=0, and y-z+4=0 Find the angle between the...

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  18. The volume of a right triangular prism ABCA(1)B(1)C(1) is equal to 3 c...

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  19. Find the multiplication of 34×0

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  20. Let OABC be a regular tetrahedron with side length unity, then its vol...

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