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If A B C D is quadrilateral and Ea n dF ...

If `A B C D` is quadrilateral and `Ea n dF` are the mid-points of `A Ca n dB D` respectively, prove that ` vec A B+ vec A D` +` vec C B` +` vec C D` =4 ` vec E Fdot`

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If A B C D is quadrilateral and E and F are the mid-points of AC and BD respectively, prove that vec A B+ vec A D + vec C B + vec C D =4 vec E Fdot

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A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD C respectively, then express vec A La n d vec A M in terms of vec A Ba n d vec A D . Also, prove that vec A L+ vec A M=3/2 vec A Cdot

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If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

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RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. Using vector method, prove that the line segments joining the mid-p...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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