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If `O` is a point in space, `A B C` is a triangle and `D , E , F` are the mid-points of the sides `B C ,C A` and `A B` respectively of the triangle, prove that ` vec O A` + ` vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot`

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RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. Show that the sum of three vectors determined by the medians of a t...

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  2. A B C D is parallelogram and P is the point of intersection of its dia...

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  3. If O is a point in space, A B C is a triangle and D , E , F are ...

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  4. Show that the point 2 hat i ,- hat i-4 hat j and - hat i+4 hat j fr...

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  5. If vec a be the position vector whose tip is (5,-3), find the c...

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

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  7. A B C D are four points in a plane and Q is the point of interse...

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  8. If vec aa n d vec b are non-collinear vectors, find the value of x fo...

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  9. The projection of a vector on the coordinate axes are (6,-3,2) Find ...

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  10. If vec a , vec b, vec c are three non- null vectors such that any tw...

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  11. Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n...

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  12. Show that the points A ,B ,C with position vectors -2 vec a+3 vec b+5 ...

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  13. Prove that the line joining the mid-points of the diagonals of a trape...

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  14. Prove that the segment joining the middle points of two non-paralle...

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  15. Using vector method, prove that the line segments joining the mid-p...

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  16. If the points with position vectors 60 hat i+2 hat j , 40 hat i-8 hat ...

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  17. If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n d...

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  18. If D and E are the mid-points of sides AB and AC of a triangle A B C r...

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  19. If G is the centroid of a triangle A B C , prove that vec G A+ vec G ...

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

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