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If bara, barb, barc form a left handed o...

If `bara, barb, barc` form a left handed orthogonal system and `bara. bara= 4, barb . barb = 9, barc . barc = 16` then `[barabarbbarc]` =

A

24

B

`-24`

C

12

D

`-12`

Text Solution

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The correct Answer is:
B
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A : If bara, barb, barc form a left handed orthogonal system such that bara.bara= 4, barb.barb =9, barc.barc =16 rArr [barabarbbarc]=-24 R : For left handed system [bara barb barc] bara, barb, barc, [barabarbbarc] =pm(absbara.absbarb.absbarc) The correct answer is

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Show that [2bara +barb +barc bara +2barb +barc bara +barb +2barc] = 4[bara barb barc]

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AAKASH SERIES-MULTIPLE PRODUCT OF VECTORS-EXERCISE -II
  1. If bara = 2bari - barj, barb = 4barj + bark, barc = 3bark then (2bara ...

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  2. For non-zero vectors bara,barb,barc,abs(baraxxbarb.barc)=abs(bara)abs(...

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  3. If bara, barb, barc form a left handed orthogonal system and bara. bar...

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  4. bara=bari-bark,barb=xbari+barj+(1-x)bark,barc=ybari+xbarj+(1+x-y)bark ...

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  5. If bara, barb, barc is a right handed system, barb is perpendicular to...

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  6. If alpha, beta, gamma are angles of a triangle then [tanalphabari+barj...

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  7. If barA=(1,a,a^(2)),barB=(1,b,b^(2)),barC=(1,c,c^(2)) are non-coplanar...

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  8. Show that the four points with position vectors bara,barb,barc,bard ar...

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  9. Let bara=bari-2barj+3bark,barb=2bari+3barj-bark,barc=lamdabari+barj+(2...

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  10. Let bara=bari+barj+bark,barb=bari-barj+2bark,barc=xbari+(x-2)barj-bark...

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  11. If baraxxbarr=barb+lamdabara,bara.barr=3, where bara=2~i+barj-bark,bar...

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  12. If baraxxbarr=barb+lamdabara, bara.barr=3, abs(bara)=1, barb.barr=

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  13. Let barb = 2bari + barj - bark, barc = bari + 3bark . If veca is a uni...

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  14. Let a=2bari + barj-bark and barb = barI +3bark. If barc is a unit vect...

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  15. Let bara=bari-barj,barb=barj-bark,barc=bark-bari. lf dis a unit vector...

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  16. A unit vector in the plane of the vectors 2bari +barj+bark, bari - bar...

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  17. The value of 'a' so that the volume of parallelopiped formed by bari +...

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  18. The volume of parallelopiped with edges bar(OA) = (lamda+ 2)bari +(l...

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  19. If bara, barb, barc are three non-coplanar vectors represented by conc...

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

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