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If V is the volume of the parallelopiped...

If V is the volume of the parallelopiped having three coterminous edge, as, `bara ,barb` and `barc` then the volume of the parallopiped having three coterminous edges as
`baralpha=(bara.bara)bara+(bara.barb)barb+(bara.barc)barc`
`barbeta=(barb.bara)bara+(barb.barb)barb+(barb.barc)barc`
`bargamma=(barc.bara)bara+(barc.barb)barb+(barc.barc)barc` is

A

V

B

`V^(2)`

C

`V^(3)`

D

`V^(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
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If [bara barb barc ] = 1 then show that (bara.bara)(barbxxbarc)+ (bara.barb)(barcxxbara)+(bara.barc)(baraxxbarb)=bara .

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AAKASH SERIES-MULTIPLE PRODUCT OF VECTORS-EXERCISE -II
  1. If bara, barb, barc are three non-coplanar vectors represented by conc...

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  2. If [a b c] = 3, then the volume (in cube units) of the parallelopiped ...

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  3. If V is the volume of the parallelopiped having three coterminous edge...

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  4. The volume of the triangular pyramid with vertices A(2, 2, 2), B(4, 3,...

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  5. If bara, barb, barc are non-coplanar, nonzero vectors and barr is any ...

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  6. If bara,barb are non-zero and non-collinear vectors then [bara barb ba...

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  7. Let barr be a vector perpendicular to bara + barb + barc . If barr=l(b...

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  8. Let bara,barb are two unit vectors such that bara.barb=0. If barc=xbar...

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  9. If bara, barb, barc are non - coplanar vectors and lamda is a real num...

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  10. If bar(a), bar(b), bar(c) are non coplanar vectors and lambda is a rea...

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  11. If bara, barb, barc are three non-coplanar vectors, barp=(barbxxbarc...

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  12. If bar(a^(1)),bar(b^(1)),bar(c^(1)) represents the reciprocal system o...

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

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  14. bara^(1)xxbarb^(1)+barb^(1)xxbarc^(1)+barc^(1)xxbara^(1)=

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  15. If barr is any vector then barr =

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  16. Arrange the following in the descending order of magnitude (A) [I...

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  17. A : If bara, barb, barc form a left handed orthogonal system such that...

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  18. If bari,barj,bark are orthogonal unit vector triad, then bari xx(barrx...

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  19. bari xx [(baraxxbarb)xxbari] +barj xx [(baraxx barb)x barj] + bark xx ...

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  20. bara, barb, barc are three unit vectors, barb is not parallel to barc ...

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