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Statement-I : The coordinates of a point...

Statement-I : The coordinates of a point equidistant from the four point (a,0,0),(0,b,0),(0,0,c),(0,0,0) are `(a/4,b/4,c/4)`
Statement-II : The distance between the origin and the centroid for the tetrahedron where vetrtice are (0,0,0),(a,0,0),(0,b,0),(0,0,c) is `(sqrt(a^(2)+b^(2)+c^(2)))/4`
Which of the above statements is correct :

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-3D-COORDINATE SYSTEM-PRACTICE EXERCISE
  1. If the origin is the centroid of the tetrahedron for which (2,-1,3),(-...

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  2. In the tetrahedrom ABCD, A=(1,2,-3) and G=(-3,4,5) is cntroid of tetra...

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  3. The circumcentre of the triangle formed by the points (1,2,3), (2,3,1)...

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  4. Statement-I : The coordinates of a point equidistant from the four poi...

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  5. The incentre of the triangle formed by (0,0,0),(3,0,0),(0,4,0) is

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  6. The centroid of the triangle formed by the points (2,-1,1),(1,-3,-5),(...

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  7. A (3,4,5), C(-1,6,1) are the vetrices of a triangle then Statement-I...

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  8. The distance between the circumcentre and the orthocentre of the trian...

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  9. If the Internal bisector of angleAOB where 0=(0,0,0), A =(3,4,12), B=(...

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  10. Statement-I : If (2,3,5),(3,5,2) and (5,2,3) are the vertices of a tri...

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  11. Locus of x^(2)+y^(2)+z^(2)=0 is

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  12. The locus of a point for which the sum the squares of the ditance from...

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  13. Show that the point whose distance from Y-axis in thrice its distance ...

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  14. ABC is a right angled triangle right angled at A. If B(2,0,2) and C(0,...

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  15. The locus of the point P such that PA^(2)+PB^(2)=10 where A=(2,3,4), B...

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  16. The locus of the point P such that PA^2+PB^2=2PC^2 where A=(1,3,2),B=(...

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  17. If the locus of a point which is equidistant form (2,3,-1) and (-3,4,-...

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  18. The coordinates of the point (3,-7,5) in the new system when the origi...

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  19. The transformed eqution of x^(2)+y^(2)+z^(2)-6x-8y+2z+24 = 0 when the ...

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  20. The line passing through the points (5,1,a) and (3,b,1) cross the yz -...

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