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If veca xx (vec b xx vecc) is perpendicu...

If `veca xx (vec b xx vecc)` is perpendicular to `(veca xx vecb ) xx vecc`, we may have

A

`(veca.vecb)|vecb|^(2)= (veca.vecb)(vecb.vecc)`

B

`veca.vecb=0`

C

`veca.vecc=0`

D

`vecb.vecc=0`

Text Solution

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The correct Answer is:
a,c
`vecaxx(vecbxxvecc)= (veca.vecc)vecb-(veca.vecb)vecb]and (vecaxx vecb) xxvecc=-(vecc. vecb) veca + (veca.vecc)vecb`
we have been givn
`(veca xx (vecbxx vecc)). ((vecaxxvecb)xxvecc)=0`
` or (veca . vecc)^(2)|vecb|^(2)- (veca.vecc)(vecb.vecc) (veca.vecb)`
` - (veca.vecb) (veca.vecc)(vecb.vecc)+ (veca.vecb)(vecb.vecc)(vecc.veca)=0`
`or (veca.vecc)^(2)|vecb|^(2)= (veca.vecc)(veca.vecb)(vecb.vecc)`
`or (veca.vecc)((veca.vecc)(vecb.vecb)- (veca.vecb) (vecb.vecc))=0`
`veca.veca=0 or (veca.vecc) |vecb|^(2) = (veca.vecb)(vecb.vecc)`
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CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

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  2. If vectors veca and vecb are two adjecent sides of a paralleogram, the...

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  3. If veca xx (vec b xx vecc) is perpendicular to (veca xx vecb ) xx vecc...

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  4. Let veca , vecb and vecc be vectors forming right- hand triad . Let ve...

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  5. a(1), a(2),a(3) in R - {0} and a(1)+ a(2)cos2x+ a(3)sin^(2)x=0 " for ...

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  6. If veca and vecb are two vectors and angle between them is theta , the...

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  7. Let veca and vecb be two non- zero perpendicular vectors. A vector vec...

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  8. If vector vec b=(t a nalpha,-1, 2sqrt(sinalpha//2))a n d vec c=(t a n...

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  9. Let vecr be a unit vector satisfying vecr xx veca = vecb, " where " |v...

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  10. If veca and vecb are unequal unit vectors such that (veca - vecb) xx[ ...

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  11. If veca and vecb are two unit vectors perpenicualar to each other and ...

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  12. If vectors veca and vecb are non collinear then veca/(|veca|)+vecb/(|v...

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

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

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

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

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

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  18. if side vec(AB) of an equilateral triangle ABC lying in the x-y plane ...

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  19. The angles of a triangle , two of whose sides are respresented by vect...

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  20. veca ,vecb and vecc are unimodular and coplanar. A unit vector vecd is...

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