41.ABCD is a quadrilateral and O is any point in its plane. Show that it then O is the point of intersection of lines joining the middle points of the opposite sides of ABCD.
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42.For any two vectors , prove that (i) (ii) (iii)
If and , show that (i) have the same direction and (ii) have opposite direction and
Here and (i)
Also, (ii)
Also,
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Short Answer Type
44.Show that the line joining the middle points of the consecutive sides of a quadrilateral is a parallelogram.
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Long Answer Type
45.In the figure, M is the mid-point of AB and N is the mid-point of CD and O is the mid-point of MN. Prove that (i) (ii)
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46.Prove by vector method that the line segment joining the mid-points of the diagonals of trapezium is parallel to the parallel sides and equal to help of there difference.
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47.ABCD is a parallelogram. If L and M are the mid-point of BC and DC respectively, then express in terms of .
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48.ABCDEF is a regular hexagon. Show that (i) (ii) where O is centre of the hexagon.
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49.Prove that the sum of all the v ectors from the centre of a regular octagon to its vertices is the zero vector.
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50.Show that the sum of three vector determined by the medians of a triangle directed from the vertices is zero.
Long Answer Type
then O is the point of intersection of lines joining the middle points of the opposite sides of ABCD.
Short Answer Type
in terms of 
.
, prove that
(ii) 
(iii) 
and 
, show that
have the same direction and 
have opposite direction and 
and 
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