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If (veca xx vecb) xx (vecc xx vecd) . (v...

If `(veca xx vecb) xx (vecc xx vecd) . (veca xx vecd) =0` then which of the following may be true ?

A

A. `veca, vecb and vecd` are nenessarily coplanar

B

B. `veca` lies iin the plane of `vecc and vecd`

C

C. `vecb` lies in the plane of `veca and vecd`

D

D. `vecc` lies in the plane of `veca and vecd`

Text Solution

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The correct Answer is:
b,c,d
`(vecaxxvecb )xx(vecc xx vecd). (vecaxxvecd) =0`
`or ([veca vecc vecd] vecb- [vecb vecc vecd]veca) . (veca xx vecd)=0`
`or [veca veccvecd] [vecb veca vecd] =0`
Hence, either `vecc or vecb` must lie in the plane of ` veca and vecd`.
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. If side vec A B of an equilateral trangle A B C lying in the x-y plan...

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  2. The angles of triangle, two of whose sides are represented by vector...

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  3. vec a , vec b ,a n d vec c are unimodular and coplanar. A unit vector ...

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  4. If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc...

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  5. Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(vec...

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  6. if veca xx vecb = vecc ,vecb xx vecc = veca , " where " vecc ne vec0 ...

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  7. Let veca, vecb, and vecc be three non- coplanar vectors and vecd be a ...

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  8. If vec a , vec b , a n d harr c are three unit vecrtors such that ...

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  9. If in triangle ABC, vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (...

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  10. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

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  11. The scalars l and m such that l vec a+m vec b= vec c ,where vec a , v...

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  12. If (veca xx vecb) xx (vecc xx vecd) . (veca xx vecd) =0 then which of ...

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  13. A ,B ,Ca n dD are four points such that vec A B=m(2 hat i-6 hat j+2 h...

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  14. If the vectors vec a, vec b, vec c are non-coplanar and l,m,n are dist...

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  15. Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(...

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  16. If vectors vec A=2 hat i+3 hat j+4 hat k , vec B= hat i+ hat j+5 hat ...

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  17. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc=...

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  18. If veca xx (vecbxx vecc)= (veca xx vecb)xxvecc then

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  19. A vector (vecd) is equally inclined to three vectors veca= hati - hatj...

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  20. A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, ...

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