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Let veca vecb and vecc be non- zero vect...

Let `veca vecb and vecc` be non- zero vectors aned `vecV_(1) =veca xx (vecb xx vecc) and vecV_(2) = (veca xx vecb) xx vecc`.vectors `vecV_(1) and vecV_(2)` are equal . Then

A

`veca and vecb` ar orthogonal

B

`veca and vecc` are collinear

C

`vecb and vecc` ar orthogonal

D

`vecb= lambda (veca xx vecc) " when " lambda ` is a scalar

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The correct Answer is:
b,d
`vecV_(1) = vecV_(2)`
`vecaxx (vecbxxvecc) = (vecaxxvecb)xxvecc`
`or (veca.vecc)vecb - (veca.vecb)vecc= (veca.vecc)vecb- (vecb.vecc)veca`
`or (veca .vecb)vecc = (vecb.vecc)veca`
Thus , either `vecc and veca` ar collinear or `vecb` is perpendicular to both `veca and vecc Rightarrow vecb = lamda (veca xx vecc) `
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. If vectors veca and vecb are non collinear then veca/(|veca|)+vecb/(|v...

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  2. If veca and vecb are non - zero vectors such that |veca + vecb| = |vec...

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  3. Let veca vecb and vecc be non- zero vectors aned vecV(1) =veca xx (vec...

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  4. Vectors vecA and vecB satisfying the vector equation vecA+ vecB = vec...

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  5. A vector vec d is equally inclined to three vectors vec a= hat i+ ...

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  6. Vectors Perpendicular to hati - hatj- hatk and in the plane of hati + ...

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  7. If side vec A B of an equilateral trangle A B C lying in the x-y plan...

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

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

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

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

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

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

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

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

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

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

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

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

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