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A : If (2,1,-3) , (-2,3,4) , (1,2,2) ar...

A : If `(2,1,-3) , (-2,3,4) , (1,2,2) ` are the midpoints of `bar(BC) ,bar( CA), bar(AB)` of `DeltaABC` then `A=(-3,4,9)`
R : If `(alpha_1,beta_1,gamma_1), (alpha_2,beta_2,gamma_2),(alpha_3,beta_3,gamma_3)` are the midpoints of the sides `bar(BC),bar(CA),bar(AB)` of `DeltaABC` then `A=(alpha_2+alpha_3-alpha_1,beta_2+beta_3-beta_1,gamma_2+gamma_3-gamma_1)`

A

(0,5/2,5/3)

B

(5,0,-5)

C

(-1,2,-1)

D

(1,6,3)

Text Solution

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DIPTI PUBLICATION ( AP EAMET)-COORDINATE SYSTEM (3D)-EXERCISE 1
  1. If the orthocentre and the circucentre of a triangle are (-3,5,1),(3,3...

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

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  3. A : If (2,1,-3) , (-2,3,4) , (1,2,2) are the midpoints of bar(BC) ,ba...

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  4. The points D,E,F are the midpoints of the sides bar(BC),bar(CA),bar(AB...

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  5. D(2,1,0) ,E(2,0,0),F(0,1,0) are midpoints of the sides BC,CA,AB of De...

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  6. In DeltaABC the mid-point of the sides AB,BC and CA are respectively (...

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  7. If the extremities of a diagonal of square are (1,-2,3),(2,-3,5) then ...

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  8. If (5,7,10),(1,9,6) are the extremities of the hypotenuse of a right a...

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  9. The circumradius of the triangle formed by the points (2,-1,1),(1,-3,-...

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

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

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  12. If the points (3,2,-4) ,(5,4k),(9,8-10)are collinear then k =

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  13. If (k,1,5) ,(1,0,3),(7,-2,1) are collinear then (k,-1)=

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  14. The locus of a point which is at a distance of 5 unit from (2,1,-3) is

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  15. The locus of a point which is at a distance of 2 unit from yz - plane ...

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  16. The locus of the point which is equidistant from xy plane and yz - pla...

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  17. The locus of point which is equidistant from the points (-2,2,3),(3,...

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  18. The locus of a point for which the sum of the squares of the distances...

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  19. The locus of a point P from which the distance to the point (1,1,1) is...

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  20. The locus of a point P from which the distance to the point (2,3,-1) i...

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