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If the vectors (a, b, c), (b, c, a) and ...

If the vectors (a, b, c), (b, c, a) and (c, a, b) are linealy dependent then

A

`a^(3)+b^(3)+c^(3)=3abc`

B

`a^(2)+b^(2)+c^(2)=2abc`

C

`a^(3)+b^(3)+c^(3)+3abc=0`

D

`a^(2)+b^(2)+c^(2)+2abc=0`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-MULTIPLE PRODUCT OF VECTORS-PRACTICE EXERCISE
  1. If bara, barb, barc are the sides of a triangle ABC then [barabarb bar...

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  2. If the vectors abari+barj+bark,bari+bbarj+bark,barI+barj+cbarK are cop...

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  3. If the vectors (a, b, c), (b, c, a) and (c, a, b) are linealy dependen...

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  4. The volume of a parallelopiped whose edges are represented by -12bari+...

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  5. The volume of the rectangular box whose coterminal edges along axes of...

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  6. If barx.bara=barx.barb=barx.barc=0 for some non-zero vector barx and a...

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  7. The volume of the tetrahedron having the edges barI+2barj-bark,bari+ba...

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

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  9. Which of the following statement is not true

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  10. If bara is perpendicular to barbxxbarc, then which of the following is...

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  11. barixx(barjxxbark)+barjxx(barkxxbari)+barkxx(barixxbarj)=

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  12. barixx(barixxbara)+barjxx(barjxxbara)+barkxx(barkxxbara)=

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  13. If barb, barc are like unit vectors and baraxx (barbxx barc) = bar0 th...

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  14. If bara, barb are two unit perpendicular vectors then baraxx (baraxx b...

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  15. If [baraxx(barbxxbarc)]xxbarc=(bara·barc)barR then barR=

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  16. If bara and barb are unit vectors, then the vector ( bara + barb) xx (...

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  17. If barp is non- · zero vector such that barp. bara= barp. barb = 0 and...

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  18. If (bara xx barb).(barc xx bard) = (bara.barc)(barb.bard) + k(bara.bar...

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  19. If (baraxxbarb)xx(barcxxbard)=[barabarbbard]barc +kbard then k =

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  20. The volume of tetrahedron with edges barixxbarj,barjxxbark,barkxxbari ...

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