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If veca and vecb are two unit vectors in...

If `veca and vecb` are two unit vectors inclined at an angle `pi//3 then { veca xx (vecb+veca xx vecb)} .vecb` is equal to

A

`(-3)/4`

B

`1/4`

C

`3/4`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
a
` { veca xx (vecb + veca xx vecb)} .vecb`
` { veca xx vecb + veca xx (veca xx vecb)} .vecb`
`= [veca vecb vecb] = {( veca.vecb) veca - (veca .veca) (vecb.vecb)`
` cos^(2) pi/3 -1 = -3/4`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y...

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

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

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

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

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  7. The condition for equations vecrxxveca = vecb and vecr xx vecc = vecd ...

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  8. If veca=2hati + hatj + hatk,vecb=hati + 2hatj + 2hatk ,vecc= hati + ha...

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

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

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

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

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

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

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

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  16. If V be the volume of a tetrahedron and V ' be the volume of anothe...

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

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

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

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

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