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Let bara ,barb,barc be non coplanar vect...

Let `bara ,barb,barc` be non coplanar vectors and `bara^(1)=(barbxxbarc)/([barabarbbarc]),barb^(1)=(barcxxbara)/([barabarbbarc])` and `barc^(1)=(baraxxbarb)/([barabarbbarc])` then prove that
`(bara+barb).bara^(1)+(barb+barc).barb^(1)+(barc+bara).barc^(1)=3`

A

`bar0`

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
D
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If bara, barb, barc are three non-coplanar vectors, barp=(barbxxbarc)/([bara barb barc]),barq=(barcxxbara)/([bara barb barc]),barr=(baraxxbarb)/([bara barb barc]) then (bara+barb).barp+(barb+barc).barq+(barc+bara).barr =

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AAKASH SERIES-MULTIPLE PRODUCT OF VECTORS-PRACTICE EXERCISE
  1. bara,barb,barc are non-coplanar and barl=(barbxxbarc)/([bara barb barc...

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  2. bara.barb^(1)+barb.barc^(1)+barc.bara^(1)=

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  3. Let bara ,barb,barc be non coplanar vectors and bara^(1)=(barbxxbarc)/...

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  4. baraxxbara^(1)+barbxxbarb^(1)+barcxxbarc^(1)=

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  5. The vector [(bari-barj)xx(barj-bark)]xx(bari+5bark) is

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  6. Let bara,barb,barc be three vectors which satisfy baraxx(barbxxbarc)=(...

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  7. If bara=bari+barj+bark,bara.barb=1,baraxxbarb=2bari+barj-3bark then 3b...

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  8. Unit vector coplanar with bari+barj+2bark,bari+2barj+bark and perpendi...

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  9. If bara,barc,bard are coplaner then the value of (bard+bara).[baraxx{b...

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  10. Let bara, barb, barc be three vectors having magnitudes 1,1,2 respecti...

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  11. If bara,barb,barc are non-coplanar unit vectors such that baraxx(barbx...

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  12. Vector component of barb perpendicular to bara is

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  13. The vector equation of the plane passing through the points (1, -2, 5)...

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  14. Equation of the plane passing through the points with position vector...

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  15. Vector equation of the plane passing through bara, barb and parallel t...

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  16. The shortest distance between the straight line passing through the po...

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  17. The distance between the plane whose equation is barr · (2bari + barj-...

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  18. The vector equation of a straight line passing through bara and perpen...

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  19. If bara,barb,barc are the position vectors of the vertices of a triang...

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  20. Vector equation of the plane passing through the line barr =bara+ alph...

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