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If points (1,2,3), (0,-4,3), (2,3,5) and...

If points (1,2,3), (0,-4,3), (2,3,5) and (1,-5,-3) are vertices of tetrahedron, then the point where lines joining the mid-points of opposite edges of concurrent is

A

`(1,-1,2)`

B

`(-1,1,2)`

C

(1,1,-2)

D

`(-1,1,-2)`

Text Solution

Verified by Experts

The correct Answer is:
A

We know that line joining the mid-points of opposite edges of tetrahedron are concurrent at point, which is the mean of vertices of tetrahedron. Here it is `(1,-1,2)`
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CENGAGE-VECTORS; DEFINITION, GEOMETRY RELATED TO VECTORS-DPP 1.1
  1. ABCDEF is a regular hexagon in the x-y plance with vertices in the ant...

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  2. Let position vectors of point A,B and C of triangle ABC represents be ...

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  3. If D,E and F are the mid-points of the sides BC, CA and AB respectivel...

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  4. If points (1,2,3), (0,-4,3), (2,3,5) and (1,-5,-3) are vertices of tet...

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  5. The unit vector parallel to the resultant of the vectors 2hati+3hatj-h...

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  6. ABCDEF is a regular hexagon. Find the vector vec AB + vec AC + vec AD ...

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  7. If veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7 , then find the ang...

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  8. If sum of two unit vectors is a unit vector; prove that the magnitude ...

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  9. The position vectors of the points A,B, and C are hati+2hatj-hatk, hat...

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  10. Orthocenter of an equilateral triangle ABC is the origin O. If vec(OA)...

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  11. If the position vectors of P and Q are hati+2hatj-7hatk and 5hati-3hat...

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  12. The non zero vectors veca,vecb, and vecc are related byi veca=8vecb n...

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  13. The unit vector bisecting vec(OY) and vec(OZ) is

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  14. A unit tangent vector at t=2 on the curve x=t^(2)+2, y=4t-5 and z=2t^(...

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  15. If veca and vecb are position vectors of A and B respectively, then th...

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  16. Let veca=(1,1,-1), vecb=(5,-3,-3) and vecc=(3,-1,2). If vecr is collin...

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  17. A line passes through the points whose position vectors are hati+hatj-...

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  18. Three points A,B, and C have position vectors -2veca+3vecb+5vecc, veca...

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  19. Three points A,B, and C have position vectors -2veca+3vecb+5vecc, veca...

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  20. Three points A,B, and C have position vectors -2veca+3vecb+5vecc, veca...

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