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If [veca vecb vecc]=1 then (bara.(barb...

If `[veca vecb vecc]=1` then
`(bara.(barbxxbarc))/((barcxxbara).barb)+(barb.(barcxxbara))/((baraxxbarb).barc)+(barc.(baraxxbarb))/((barbxxbarc).bara)=`

A

3

B

1

C

`-1`

D

0

Text Solution

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The correct Answer is:
A
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baraxx(barbxxbarc)+barbxx(barcxxbara)+barcxx(baraxxbarb)=

(barbxxbarc).(axxbard)+(barcxxbara).(barbxxbard)+(baraxxbarb).(barcxxbard)=

[ (baraxxbarb)xx(barbxxbarc)(barbxxbarc)xx(barcxxbara)(barcxxbara)xx(baraxxbarb)] =

Show that (baraxx(barbxxbarc))xxbarc=(bara.barc)(barbxxbarc) and ((baraxxbarb).(baraxxbarc)+bara.barb)(bara.barc)=(bara.bara)(barb.barc)

barc.(barb+barc)xx(bara+barb+barc)=

The vectors baraxx(barbxxbarc),barbxx(barcxxbara).barcxx(baraxxbarb) are

If [bara barb barc ] = 1 then show that (bara.bara)(barbxxbarc)+ (bara.barb)(barcxxbara)+(bara.barc)(baraxxbarb)=bara .

Show that (bara+barb).(barb+barc)xx(barc+bara)=2[barabarbbarc]

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 [barabarbbarc][bara^(1)barb^(1)barc^(1)]=1

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

AAKASH SERIES-MULTIPLE PRODUCT OF VECTORS-PRACTICE EXERCISE
  1. If bara.bari = 4 then (bara xx barj).(2barj - 3bark) =

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  2. [baribarjbark]+[barjbarkbari]+[barkbaribarj]+[baribarkbarj]+[barjbarib...

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  3. If [veca vecb vecc]=1 then (bara.(barbxxbarc))/((barcxxbara).barb)+(...

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  4. If bara,barb,barc are non-coplanar vectors and (bara+2barb+barc).(bara...

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  5. If bara, barb, barc are the sides of a triangle ABC then [barabarb bar...

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

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

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

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

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

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

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

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  13. Which of the following statement is not true

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

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

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

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

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

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

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

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