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If |veca|=2 and |vecb|=3 and veca.vecb=0...

If `|veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(vecaxx(vecaxxvecb))))` is equal

A

`48 hatb`

B

`-48 hatb`

C

`48 hata`

D

`-48 hata`

Text Solution

Verified by Experts

The correct Answer is:
a
`(vecaxx (veca xx (veca xx (vecaxx vecb ))))`
` = (vecaxx (veca xx ((veca .vecb)veca -(veca .vecb)vecb)))`
`(veca xx (veca xx (-4vecb)))`
` -4 (veca xx (veca xx vecb))`
` -4 ((veca xx vecb) veca - (veca.veca)vecb)`
` -4 (-4vecb) = 16 vecb = 48 vecb`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

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  2. If vecd=vecaxxvecb+vecbxxvecc+veccxxveca is a on zero vector and |(vec...

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  3. If |veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(veca...

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  4. If two diagonals of one of its faces are 6hati + 6 hatk and 4 hatj + ...

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  5. The volume of a tetrahedron fomed by the coterminus edges veca , vecb ...

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  6. If veca ,vecb and vecc are three mutually orthogonal unit vectors , th...

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  7. vector vecc are perpendicular to vectors veca= (2,-3,1) and vecb= (1,...

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  8. Given veca=xhati+yhatj+2hatk,vecb=hati-hatj+hatk , vecc=hati+2hatj, ve...

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  9. Let veca=a(1)hati+a(2)hatj+a(3)hatk, vecb=b(1)hati+b(2)hatj+b(3)hatk a...

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  10. Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr....

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  11. If veca, vecb and vecc are such that [veca vecb vecc] =1, vecc= lambda...

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  12. If 4veca+5vecb+9vecc=0 " then " (vecaxxvecb)xx[(vecbxxvecc)xx(veccxxve...

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  13. Value of [vec a xx vec b,vec a xx vecc,vec d] is always equal to

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  14. Let hata and hatb be mutually perpendicular unit vectors. Then for an...

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  15. Let veca and vecb be unit vectors that are perpendicular to each other...

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  16. veca and vecb are two vectors such that |veca|=1 ,|vecb|=4 and veca. V...

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  17. Then for any arbitary vector veca, (((veca xx vecb) + (veca xx vecb))...

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  18. If veca .vecb =beta and veca xx vecb = vecc ," then " vecb is

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  19. If a(vecalphaxxvecbeta)=b(vecbetaxxvecgamma)+c(vecgammaxxvecalpha)=vec...

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  20. If (vecaxxvecb)xx(vecbxxvecc)=vecb, where veca,vecb and vecc are non z...

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