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A variable plane cutting coordinate axes...

A variable plane cutting coordinate axes in A, B, C is at a constant distance from the origin. Then the locus of centroid of the `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 cutting coordinate axes in A, B, C is at a constant d...

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  4. Equation of any plane containing the line (x-x1)/(a)=(y-y1)/(b)=(z-z1)...

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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. Consider the plane through (2, 3, -1) and at right angles to the vecto...

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  8. A plane passes through a fixed point (a, b, c) and cuts the axes in A,...

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

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  10. Consider the lines x=y=z and line 2x+y+z-1=0=3x+y+2z-2, then

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  11. If p1, p2, p3 denote the perpendicular distance of the plane 2x-3y+4z+...

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  12. A line segment has length 63 and direction ratios are 3, -26. The comp...

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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. A rod of length 2units whose one end is (1, 0, -1) and other end touch...

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  17. Consider the planes p1: 2x+y+z+4=0, p2: y-z+4=0 and p3: 3x+2y+z+8=0 ...

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  18. The volume of a tetrahedron prism ABCA1B1C1 is equal to 3. Find the co...

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  19. If the plane passing through the origin and parallel to the line (x-1)...

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

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