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If 4 vec a+5 vec b+9 vec c=0, then ( vec...

If `4 vec a+5 vec b+9 vec c=0,` then `( vec axx vec b)xx[( vec bxx vec c)xx( vec cxx vec a)]` is equal to a. vector perpendicular to the plane of`a ,b ,c` b. a scalar quantity c. ` vec0` d. none of these

A

a vector perpendicular to the plane of `veca, vecb and vecc`

B

a scalar quantity

C

`vec0`

D

none of these

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The correct Answer is:
c
`4 veca + 5 vecb + 9 vecc =0`
`Rightarrow "vcectors" veca,vecb and vecc` are coplanar.
`Rightarrow vecb xx vecc and vecc xx veca` are collinear.
`Rightarrow (vecb xx vecc) xx (vecc xx veca) = vec0`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr....

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

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  3. If 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)...

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  4. Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec...

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  5. Let vec aa n d vec b be mutually perpendicular unit vectors. Then f...

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

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

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

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

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  10. If a( vecalphaxx vecbeta)+b( vecbetaxx vecgamma)+c( vecgammaxx vecalph...

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  11. If veca xx vecb = vecb xx vecc ne 0 where veca , vecb and vecc are co...

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  12. If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and...

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  13. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y...

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  14. If veca and vecb are two unit vectors inclined at an angle pi//3 then ...

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  15. If veca and vecb are othogonal unit vectors, then for a vector vecr no...

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  16. If veca+vecb ,vecc are any three non- coplanar vectors then the equa...

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  17. Sholve the simultasneous vector equations for vecx aedn vecy: vecx+vec...

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  18. The condition for equations vec rxx vec a= vec ba n d vec rxx vec c...

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  19. If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2h...

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  20. If veca=2hati + hatj+ hatk, vecb= hati+ 2hatj + 2hatk,vecc = hati+ hat...

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