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By vector method show that the figure fo...

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

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Show that the figure formed by joining the midpoints of sides of a rhombus successively is a rectangle.

Prove that the quadrilateral formed by joining the mid-points successively of any quadrilateral is also a parallelogram. Also, prove that the perimeter of that parallelogram is equal to the sum of that quadrilateral's diagonals.

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.

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.

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.

Prove that the quadrilateral formed by joining the mid-points of the sides of a square is also a square.

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 area of the parallelogram produced by joining the mid-points of the sides of a quadrilateral taken in order is half the area of the quadrilateral.

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 quadrilateral obtained by successively joining the mid -points of a parallelogram is also a parallelogram.

CHHAYA PUBLICATION-VECTOR-EXERCISE - LONG ANSWER TYPE QUESTIONS
  1. If vec(a)=hat(i)+hat(j)+hat(k), vec(b)=2hat(i)-hat(j)+3hat(k) " and " ...

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  2. By vector method, show that the four points (7, 2, -3), (6, 1, 4), (-3...

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  3. Find a unit vector in direction parallel to the sum of the vectors vec...

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  4. If vec(a)=2hat(i)-2hat(j)+hat(k), vec(b)=2hat(i)+3hat(j)+6hat(k) " and...

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  5. The vectors vec(a) " and " vec(b) are non-collinear. Find for what val...

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  6. Given that the points with position vectors 12hat(i)-5hat(j), 10hat(i)...

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

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  8. If the sum of two unit vectors is a unit vector, prove that the magnit...

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  9. ABCDEF is a regular hexagon. If vec(CD)=vec(a), vec(DE)=vec(b), " find...

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  10. bar(AC) " and " bar(BD) are the diagonals of the parallelogram ABCD. P...

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  11. By vector method show that the figure formed by joining the mid-points...

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  12. Defination : Unit vector

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  13. ABCD is a parallelogram and P is the midpoint of the side bar(BC). Pro...

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  14. ABCD is a parallelogram, P and Q are the mid-points of the sides bar(A...

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  15. ABCD is a parallelogram and P is the mid-point of bar(DC). If Q is a p...

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  16. D, E, F are the midpoints of the sides bar(BC), bar(CA) " and " bar(AB...

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  17. C is the midpoint of the line segment bar(AB) and O is any point outsi...

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  18. G is a point inside the plane of the triangle ABC, if vec(GA)+vec(GB)+...

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  19. The diagonals of the parallelogram ABCD intersect at E. If vec(a), vec...

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  20. By vector method prove that the straight line joining the midpoints of...

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