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If A,B,C,D are four points in space sati...

If A,B,C,D are four points in space satisfying `bar(AB).bar(CD)=k[|bar(AD)|^(2)+|bar(BC)|^(2)-|bar(AC)|^(2)-|bar(BD)|^(2)]` then k =

A

2

B

`-(1)/(2)`

C

`(1)/(2)`

D

`sqrt(2)`

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Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-APPENDICES (REVISION EXERCISE)-DOT PRODUCT OF TWO VECTORS
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  2. Let there be two points A, B on the curve y=x^(2) in the plane XOY sat...

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  3. If A,B,C,D are four points in space satisfying bar(AB).bar(CD)=k[|bar...

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  4. If the vectors barb=(tan alpha, -1, sqrt(4"sin"(alpha)/(2))), barc=(ta...

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  5. If baru and barv are unit vectors at an angle alpha and bara unit vect...

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  6. The angle between any two opposite pair of edges of a regular tetrahed...

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  7. If |veca|=2, |vecb|=3 and |2veca-vecb|=5, then |2veca+vecb| equals

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  8. If the vectors veca = hati-hatj+2hatk, vecb=2hati+4hatj+hatk and vecc=...

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  9. Let veca and vecb be two unit vectors. If the vectors vecc=hata+2hatb ...

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  10. If hata, hatb & hatc are unit vectors satisfying sqrt(3) veca-vecb=vec...

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  11. Let veca=2hati-hatj +hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2h...

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  12. Equation of sphere whose centre is at 7bari-4barj+bark and radius |3b...

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  13. The cartesian equation of the sphere whose centre is C(5, 2, 3) and w...

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  14. The centre and radius of the sphere r^(2) - 2r. (3i + 4j - 5k) + 1 = 0...

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  15. Equation of the sphere described on the join of the points bara=2bari+...

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  16. The radius of the sphere (barr-2bari+3barj-bark). (barr+3bari-barj+2b...

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  17. The cartesian equation of the sphere whose diameter end points are A(1...

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  18. Arrangement of raddi of the following spheres in de-scendin order is ...

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  19. The cartesian equation of the sphere with centre (2, -1, 3) and radi...

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  20. Radius of the sphere r^(2) -2r.(3i+4j-5k)+1=0 is

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