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If veca,vecb ,vecc are any three non- ...

If `veca,vecb ,vecc ` are any three non- coplanar vectors then the equation `[vecbxxvecc veccxxveca vecaxxvecb]x^(2) + [veca+vecb vecb+vecc vecc+veca] x+1 +[vecb-vecc vecc -veca veca -vecb] =0` has roots (A) real and distinct (B) real (C) equal (D) imaginary

A

real and distinct

B

real

C

equal

D

imaginary

Text Solution

Verified by Experts

The correct Answer is:
c
The given equation reduces to
`[veca vecb vecc] ^(2)x^(2) +2[veca vecb vecc]x+1 =0Rightarrow D =0`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. If vec aa n d vec b are two unit vectors incline at angle pi//3 , ...

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

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

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  4. Solve the simultaneous vector equations for vecx and vecy: vecx+veccxx...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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