Short Answer Type
are any four vectors in 3 - dimensional space with the same initial point and such that 
show that terminals, A, B, C, D of these vectors are coplanar. Find the point at which AC and BD meet. Find the ratio in which P divides AC and BD.
respectively are such that 
. Show that the four points are coplanar. Also, find the position vector of the point of intersection of lines AC and BD.
Long Answer TypeShort Answer TypeLong Answer Type
be the position vectors of A, B, C and D respectively with reference to O as the origin.
∴ P.V. of mid-point of diagonal BD = P.V. of mid-point of diagonal AC.
∴ diagonal AC and BD bisect each other.
(ii) Assume that the diagonals AC and BD of the quadrilateral bisect each other.
∴ P.V. of mid-point of diagonal BD = P.V. of mid-point of diagonal AC.
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