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A variable plane is at a constant distance `p` from the origin and meets the coordinate axes in `A , B , C` . Show that the locus of the centroid of the tehrahedron `O A B Ci sx^(-2)+y^(-2)+z^(-2)=16p^(-2)dot`

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MCGROW HILL PUBLICATION-THE DIMENSIONAL GEOMETRY -SOLVED EXAMPLES (NUMERICAL ANSWER TYPE QUESTIONS)
  1. Suppose A(2,3,5),B(b,3,5) and C(7,5,c) are vertices of a triangle. If ...

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  2. The plane 3x+4y+6z+7=0 is rotated about the line r=(i+2j-3k)+t(2i-3j...

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  3. Let L be a line through B(3i+j-k) and parallel 21-j+2k. Suppose A is a...

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  4. Suppose a=a(1)i+a(2)j+a(3)k is a vector which lies in the plane contai...

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  5. Suppose position vectors of A, B, C are respectively i+2j+k,2i-j+2k an...

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  6. Suppose H(3,2,-1) and C(3,2,5) are respectively the orthocentre and ci...

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  7. The direction cosines of two lines satisfy 2l+2m-n=0 and lm+mn+nl=0. T...

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  8. If equation of plane passing through (2,1,3),(3,2,1)and(1,3,2) is ax+b...

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  9. The distance of the point (-1, -5, -10) from the point of intersection...

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  10. If Q is foot of the perpendicular from the point P(4, - 5, 3) on the l...

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  11. If the lines (x-4)/15 = (y-17)/9 = (z-11)/8 and (x-15)/4 = (y-9)/17 = ...

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  12. If the root of perpendicular from A(3,1,0) on a line passing through B...

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  13. Find the angle between the lines x-3y-4=0,4y-z+5=0a n dx+3y-11=0,2y...

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  14. P,Q,R,S are the points (1,2,-2), (8,10,11), (1,2,3) and (3,5,7) respec...

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  15. The area of the triangle whose vertices are A(1,-1,2),B(2,1-1)C(3...

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  16. A plane passing through a point (1, 2, 2) and is perpendicular to two ...

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  17. A variable plane x/a+y/b+z/c=1 at a unit distance from origin cuts the...

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  18. A variable plane is at a constant distance p from the origin and meets...

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  19. Find the point where the line (x-1)/2=(y-2)/-3=(z+3)/4 meets the plane...

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  20. Let s be the distance between the lines: r=2i-j+k+t(2i+j+2k) (1) a...

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