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# Use a scalar product to show that AB is perpendicular to BC

The diagram shows a trapezium ABCD in which BA is parallel to CD. The position vectors of A. B and C relative to an origin 0 are given by

34 OA =( 0 4 ), OB =( 2 ) and O= ( 6).

(1) Use a scalar product to show that AB is perpendicular to BC. (ii) Given that the length of CD is 12 units, find the position vector of D.

[3] [4]

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