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Prove that the segment joining the middl...

Prove that the segment joining the middle points of two non-parallel sides of a trapezium is parallel to the parallel sides and half of their sum.

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RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. Show that the points A ,B ,C with position vectors -2 vec a+3 vec b+5 ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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