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[(baraxxbarb)xx(baraxxbarc)].bard=k[bara...

`[(baraxxbarb)xx(baraxxbarc)].bard=k[bara barb barc]` then k=

A

0

B

1

C

2

D

3

Text Solution

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The correct Answer is:
B
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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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Let bara ,barb,barc be non coplanar vectors and bara^(1)=(barbxxbarc)/([bara barb barc]),barb^(1)=(barcxxbara)/([bara barb barc]) and barc^(1)=(baraxxbarb)/([bara barb barc]) then prove that (bara+barb+barc).(bara^(1)+barb^(1)+barc^(1))=3

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

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AAKASH SERIES-MULTIPLE PRODUCT OF VECTORS-EXERCISE -II
  1. The shortest distance between the lines whose equations are barr = t...

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  2. The shortest distance between the lines through the points (2, 3, 1), ...

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  3. The lines barr =bara+ tbarb, barr = barc + bart^(1)bard are coplanar i...

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  4. Observe the following, choose correct answer : Assertion(A): The lin...

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  5. The equation of the plane containing the lines barr = bara+ tbarb and ...

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  6. Let bara=a(1)bari+a(2)barj+a(3)bark,barb=b(1)bari+b(2)barj+b(3)barkbar...

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  7. The three concurrent edges of a parallelopiped represents the vectors ...

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  8. The shortest distance between the skew lines barr=(bari+3barj+3barK)+t...

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  9. If x, y, z are non-zero real numbers, bara=xbari+2barj,bara=ybarj+3bar...

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  10. The angle between the lines barr=(2bari-3barJ+k)+lamda(bari+4barj+3k...

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  11. If bara=2bari +bark, barb=bari +barj+bark, barc=4bari-3barj+7bark then...

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  12. If bara,barb,barc are three vectors such that absbara =1, absbarb = ...

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  13. [(baraxxbarb)xx(baraxxbarc)].bard=k[bara barb barc] then k=

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  14. If bara=2bari-3barj+5bark,barb=3bari-4barj+5bark and barc = 5bari - 3b...

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  15. The shortest distance between the skew line (x-3)/(-1) =(y-4)/(2)=(z+2...

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  16. If veca =2bari+3barj,vecb =bari+barj+bark and vecc=lamdabari+4barj+2ba...

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  17. If the volume of parallelopiped with conterminus edges 4hati+5hatj+hat...

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  18. If vecA,vecB,vecC are three non-coplanar vectors such that abs(vecA)=4...

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  19. If bara=bari+barj+bark,barb=bari+barj,barc=bari and bar(baraxxbarb)xxb...

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  20. Let OA, OB, OC be the co-terminal edges of a rectangular parallelopipe...

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