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A point O is the centre of a circle circ...

A point `O` is the centre of a circle circumscribed about a triangle`A B Cdot` Then ` vec O Asin2A+ vec O Bsin2B+ vec O Csin2C` is equal to a. `( vec O A""+ vec O B""+ vec O C)sin2A` b. `3 vec O G ,w h e r eG` is the centroid of triangle `A B C` c. ` vec0` d. none of these

A

`(O vec a + O vec B + O vec C ) sin 2 A `

B

`3 vec(OG), ` where G is the centroid of triangle ABC

C

`vec 0`

D

none of these

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-ALGEBRA OF VECTORS-Exercise
  1. A point O is the centre of a circle circumscribed about a triangleA...

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  2. The vectors 2hati+3hatj, 5hati+6hatj and 8hati+lamdahatj have their in...

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  3. If 4 hati + 7 hat j + 8 hatk, 2 hati +3 hatj + 4 hatk and 2 hati +...

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  4. If veca is a non-zero vector of modulus a and m is a non-zero scalar, ...

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  5. D, E and F are the mid-points of the sides BC, CA and AB respectively ...

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  6. If vec a ,\ vec b ,\ vec c are the position vectors of the vertices...

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  7. If P, Q, R are three points with respective position vectors hati + ha...

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  8. Let ABC be a triangle, the position vectors of whose vertices are 7hat...

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  9. If vec a = hati + 2 hatj + 2 hat k and vec b = 3 hati + 6 hatj + 2 h...

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  10. veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b ...

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  11. The vector vec c , directed along the internal bisector of the angle...

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  12. A, B have vectors vec a , vec b relative to the origin O and X, Y d...

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  13. If a vector ofmagnitude 50 is collinear with vector vecb = 6 hat i - 8...

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  14. The vector vec c , directed along the internal bisector of the angle...

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  15. Let vec a , vec b ,vec c are three non- coplanar vectors such that ...

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  16. If vec a, vec b , vec c are three non- coplanar vectors such that v...

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  17. veca, vecb ,vecc are three non zero vectors no two of which are collon...

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  18. Let alpha,beta and gamma be distinct real numbers. The points with pos...

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  19. The points with position vectors 60hati+3hatj,40hati-8hatj, ahati-52ha...

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  20. If the points with position vectors 10 hat i+3 hat j ,12 hat i-5 ha...

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