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If veca=2hati+3hatj+hatk, vecb=hati-2hat...

If `veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk` and `vecc=-3hati+hatj+2hatk`, then `[veca vecb vecc]=`

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The correct Answer is:
b
Let `veca xx vecb = x hati + y hatj + zhatk`. Therefore,
,` [veca vecb hati] = (veca xx vecb) . Hati =x`
`[veca vecb hatj] = (veca xx vecb ) . Hatj = y `
`[veca vecb veck] = (veca xx vecb) . Hatk =z`
Hence, ` [ veca vecb hati] hati + [ veca vecb hatj] hatj`
` [ veca vecb hatk] hatk = xhati = yhatj + zhatk + veca xx vecb `
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. Solve the simultaneous vector equations for vecx and vecy: vecx+veccxx...

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

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

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  4. If veca=2hati + 3hatj+ 8hatk is perpendicular to vecb= 4hati-4hatj + a...

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  5. Let veca (x) = (sin x) hati+ (cos x) hatj and vecb(x) = (cos 2x) hati ...

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  6. For any vectors veca and vecb, (veca xx hati) . (vecb xx hati) + ( vec...

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  7. If veca,vecb and vecc are three non coplanar vectors and vecr is any v...

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  8. If vecP = (vecbxxvecc)/([vecavecbvecc]).vecq=(veccxxveca)/([veca vecb ...

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  9. A(veca),B(vecb),C(vecc) are the vertices of the triangle ABC and R(vec...

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  10. If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is ...

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  11. If V be the volume of a tetrahedron and V ' be the volume of another...

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  12. [( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)(...

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  13. If vecr=x(1)(vecaxx vecb) + x(2) (vecb xxvecc) + x(3)(vecc xxveca) and...

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  14. If veca bot vecb then vector vecv in terms of veca and vecb satisfying...

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  15. If vec a^'= hat i+ hat j , vec b^' hat i- hat j+2 hat ka n d vec c^'2...

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  16. If veca= hati +hatj, vecb= hatj + hatk, vecc = hatk + hati then in th...

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  17. If unit vectors vec a and vec b are inclined at angle 2theta such t...

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  18. vec a, vec ba n d vec c are non-collinear if vec axx( vec bxx vec c)+...

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  19. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

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  20. If vectors vec aa n d vec b are two adjacent sides of a parallelogr...

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