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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-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  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 vecd is equally inclined to three vectors veca=hati-hatj+hatk...

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  6. Vectors perpendicular tohati-hatj-hatk and in the plane of hati+hatj+h...

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  7. If the sides vec(AB) of an equilateral triangle ABC lying in the xy-pl...

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  8. Let hata be a unit vector and hatb a non zero vector non parallel to v...

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  9. veca ,vecb and vecc are unimdular and coplanar. A unit vector vecd is ...

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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 t...

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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 veca, vecb and vecc are three unit vectors such that veca xx (vecb ...

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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 lveca + m vecb =vecc, " where " veca, ve...

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

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  19. A,B C and dD are four points such that vec (AB) = m(2 hati - 6 hatj +...

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  20. If the vectors veca, vecb, vecc are non -coplanar and l,m,n are distin...

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