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Let vecb=-veci+4vecj+6veck, vecc=2veci-7...

Let `vecb=-veci+4vecj+6veck, vecc=2veci-7vecj-10veck.` If `veca` be a unit vector and the scalar triple product `[veca vecb vecc]` has the greatest value then `veca` is

A. `(1)/(sqrt(3))(hati+hatj+hatk)`
B. `(1)/(sqrt(5))(sqrt(2)hati-hatj-sqrt(2)hatk)`
C. `(1)/(3)(2hati+2hatj-hatk)`
D. `(1)/(sqrt(59))(3hati-7hatj-hatk)`

A

`(1)/(sqrt(3))(hati+hatj+hatk)`

B

`(1)/(sqrt(5))(sqrt(2)hati-hatj-sqrt(2)hatk)`

C

`(1)/(3)(2hati+2hatj-hatk)`

D

`(1)/(sqrt(59))(3hati-7hatj-hatk)`

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
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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. If veca, vecb, vecc are unit vectors such that veca+vecb+vecc=0, find...

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  19. Let A be vector parallel to line of intersection of planes P1 and P2. ...

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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. Find the 7th term of GP if the first term is 7 and common ratio is 2.

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