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If veca, vecb and vecc are any three vec...

If `veca, vecb` and `vecc` are any three vectors forming a linearly independent system, then `AA theta in R`
`vecp=vecacostheta+vecbsintheta+vecc(cos2theta)`
`vecq=vecacos((2pi)/(3)+theta)+vecbsin((2pi)/(3)+theta) + vecc(cos 2)((2pi)/(3)+theta)`
and `vecr=vecacos(theta-(2pi)/(3))+vecbsin(theta-(2pi)/(3))+vecc cos2(theta-(2pi)/(3))`
then `[vecpvecqvecr]`

A

[a b c]`costheta`

B

[a b c]`cos2theta`

C

[a b c]`cos3theta`

D

none of these

Text Solution

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The correct Answer is:
D
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ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If veca, vecb and vecc are any three vectors forming a linearly indepe...

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  2. Let O be the origin and let PQR be an arbitrary triangle. The point S ...

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  3. Let O be the origin and vec(OX) , vec(OY) , vec(OZ) be three unit vec...

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  4. Let O be the origin, and O X , O Y , O Z be three unit vectors ...

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  5. Let a, b and c be three unit vectors such that atimes(btimesc)=(sqrt(3...

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  6. Let vec a , vec b and vec c be three non-zero vectors such that no ...

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  7. If vec a , vec ba n d vec c are unit vectors satisfying | vec a- v...

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  8. The vector(s) which is/are coplanar with vectors hat i+ hat j+2 hat...

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  9. Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec ...

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  10. Two adjacent sides of a parallelogram A B C D are given by vec A B=...

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  11. Let P,Q R and S be the points on the plane with position vectors -2hat...

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  12. If aa n db are vectors in space given by vec a=( hat i-2 hat j)/(sq...

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  13. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb)*(...

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  14. The edges of a parallelopiped are of unit length and are parallel to ...

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  15. Let two non-collinear unit vectors veca and vecb form an acute angle. ...

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  16. Let the vectors PQ,OR,RS,ST,TU and UP represent the sides of a regular...

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  17. The number of distinct real values of lambda , for which the vectors...

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  18. Let veca,vecb,vecc be unit vectors such that veca+vecb+vecc=vec0. Whic...

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  19. Let vec A be a vector parallel to the line of intersection of plan...

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  20. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

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  21. The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk an...

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