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By vector method prove that the straight...

By vector method prove that the straight line joining the mid-points of the diagonals of a trapezium is parallel ot the parallel sides and half of their difference.

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Prove by vector method that the line segment joining the mid-points of the diagonals of a trapezium is parallel to the parallel sides and equal to half of their difference.

By vector method prove that the straight line joining the midpoints of two non-parallel sides of a trapezium is parallel to the parllel sides and half of their sum.

Prove that the line segment joining the mid-point of two transverse sides of a trapezium is parallel to its parallel sides.

Prove that the line segment joining the mid-points of the lateral sides of any trapezium is parallel to any of its parallel sides.

Using vector properties, show that, a straight line obtained by joining the mid-points of the oblique sides of a trapezium is parallel to the parallel sides of the trapezium and is equal to half of the sum of lengths of the parallel sides.

Prove that the line segment obtianed by joining the midpoints of two transversed sides of a trapezium is parallel to the parallel sides of the trapezium.

Show that the straight line joining the mid - points of two sides of a triangle is equal to half the third side .

Using vector method show that the line joining the middle points of two sides of a triangle is parallel and half of the third side.

Using vectors , prove that the line joining the midpoints of two sides of a triangle, is parallel to the base and half its length.

By vector method show that the figure formed by joining the mid-points of a quadrilateral is parallelogram.

CHHAYA PUBLICATION-VECTOR-ILLUSTRATIVE EXAMPLES
  1. The position vectors of the points A, B, C and D are hat(i)+hat(j)+hat...

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  2. show by vector method that the points (2, -1, 3), (3, -5, 1) and (-1, ...

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  3. Using vector method show that the points (7, 9), (3, -7) and (-3, 3) f...

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  4. The position vectors of the points A,B, and C are 2hat(i)+4hat(j)-hat(...

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  5. Write the direction ratios of the vector 2hat(i)-hat(j)-2hat(k) and he...

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  6. Find a vector of magnitude 14 in the direciton of the vector -3hat(i)+...

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  7. If vec(a) " and "vec(b) are non-collinear vectors and vec(p)=(x+4y)vec...

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  8. Prove that the points with position vectors 60hat(i)+3hat(j), 40hat(i)...

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  9. For the vectors vec(a) " and " vec(b) show that (i) abs(vec(a)+vec(b...

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  10. (i) If the position vectors of the points A, B, C be 5hat(i)+3hat(j)+...

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  11. If the magnitude of difference of two unit vectors in sqrt(3), then sh...

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  12. ABCDEF is a regular hexagon. If vec(AB)=vec(a) " and " vec(BC)=vec(b),...

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  13. Using vector method show that the diagonals of a parallelogram bisect ...

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  14. By vector method prove that the three medians of a triangle are concur...

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  15. Using vector method show that the line joining the middle points of tw...

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  16. If G be the centroid of the triangle ABC, then prove that vec(GA)+vec(...

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  17. ABCD is a quadrilateral and E is the point of intersection of the line...

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  18. By vector method prove that the straight line joining the mid-points o...

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  19. vec(a)=hat(i)+hat(j)+hat(k) " and " vec(b)=2hat(i)+hat(j)+2hat(k) repr...

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  20. Three non-zero vectors vec(a), vec(b), vec(c) are such that no two of ...

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