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Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisects each other.

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Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other

Using vector method, prove that the line segments joining the mid-points of the adjacent sides of a quadrilateral taken in order form a parallelogram.

Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the join of the middle points of its diagonals meet in a point and bisect one another

Prove that the line segments joints joining the mid-points of the adjacent sides of a quadrilateral from a parallelogram.

Show that the segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms.

Prove that the line segments joining the mid-points of the sides of a triangle from four triangles, each of which is similar to the original triangle.

i. Show that the lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent. ii. Show that the joins of the midpoints of the opposite edges of a tetrahedron intersect and bisect each other.

Prove that the line segment joining the mid-points of the diagonals of a trapezium is parallel to each of the parallel sides and is equal to half the difference of these sides.

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. Points L, M, N divide the sides BC, CA, AB of ABC in the ratio 1:4, 3:...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Find the position vector of a point A in space such that vec O A is i...

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  20. Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6)a n d D(2,-5,1...

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