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Points L, M, N divide the sides BC, CA, AB of ABC in the ratio 1:4, 3:2, 3:7 respectively. Prove thatAL + BM + CŃ is a vector parallel to CK where K divides AB in the ratio 1: 3.

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RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. If G is the centroid of a triangle A B C , prove that vec G A+ vec G ...

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  2. Prove using vectors: Medians of a triangle are concurrent.

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  3. Points L, M, N divide the sides BC, CA, AB of ABC in the ratio 1:4, 3:...

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  4. Prove using vectors: The diagonals of a quadrilateral bisect each o...

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  5. Show that the line segments joining the mid-points of opposite side...

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  6. Prove that the line segment joining the mid points of two side of a...

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  7. A vector vec r is inclined at equal to O X ,O Ya n dO Zdot If the mag...

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  8. A vector vec r has length 21 and its direction ratios are proport...

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  9. If vec a and vec b are non-collinear vectors and vectors vecalpha=(x...

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  10. A B C D is a parallelogram. E ,F are mid-points of B C ,C D respective...

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  11. If a\ a n d\ b ar non collinear vector such that x1 vec a+y1 vec b=x2 ...

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  12. Show that the vectors a, b, c given by vec a= hat i+2 hat j+3 hat k ,...

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  13. A vector vec O P is inclined to O X at 50^0 and O Y at 60^0 . Find th...

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  14. If a vector makes angles alpha,beta,gamma. with . OX ,O Ya n dO Z ...

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  15. A B C D is a parallelogram. If L and M are the mid-points of B C and D...

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  16. Find a unit vector in the direction of the resultant of the vectors...

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  17. Find the position vector of the mid-point of the vector joining the...

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  18. Show that the line joining one vertex of a parallelogram to the mid...

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  19. Let vec a , vec b, vec c be three non-zero vectors such that any two ...

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  20. If vec a , vec b are the position vectors of the points (1,-1),(-2,m...

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