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 TypeLet 
be position vectors of vertices A, B, C, D of quadrilateral ABCD.
Let P, Q, R, S be mid-points of the sides AB, BC, CD, DA respectively of quadrilateral ABCD.
position vectors of P, Q, R, S are
respectively.
Position vectors of mid - point of PR is
Position vector of mid- point of QS is
Since position vector of mid-points of PR and QS is same.
∴ lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
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