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If vec aa n d vec b are two unit vector...

If ` vec aa n d vec b` are two unit vectors incline at angle `pi//3` , then `{ vec axx( vec b+ vec axx vec b)}dot vec b` is equal to `(-3)/4` b. `1/4` c. `3/4` d. `1/2`

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 PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  3. If vec aa n d vec b are two unit vectors incline at angle pi//3 , ...

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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 and vecy: vecx+vecc...

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

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  8. If veca=2hati + hatj + hatk, vecb=hati + 2hatj + 2hatk then [veca vecb...

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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. vec ba n d vec c are unit vectors. Then for any arbitrary vector vec ...

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  13. Let vec a , vec ba n d vec c be three non-coplanar vectors and ve...

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  14. A( vec a),B( vec b)a n dC( vec c) are the vertices of triangle A B ...

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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 another...

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

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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 and vecc' = 2hati -...

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