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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+vecbvecb+veccvecc+veca] x+1 +[vecb-veccvecc -vecc-vecaveca -vecb] =0` has roots

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-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If veca and vecb are two unit vectors inclined at an angle pi//3 then ...

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

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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 + hatj+ hatk, vecb= hati+ 2hatj + 2hatk,vecc = hati+ hat...

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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) and C (vecc) are the vertices of triangle ABC and R...

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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. [(veca xxvecb)xx(vecb xx vecc) (vecb xxvecc) xx (vecc xxveca) (veccxxv...

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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 the vectors veca and vecb are perpendicular to each other then a ve...

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  18. If veca' = hati + hatj, vecb'= hati - hatj + 2hatk nad vecc' = 2hati -...

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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 veca and vecb are inclined at an angle 2 theta such th...

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