are the vertices of a rhombus.

Prove, using vectors, that its diagonals are perpendicular.  (2 marks)

Consider the rhombus    shown below, where    and    and    is a real constant.
 

1. Find  .  (1 mark)
   

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2. Show that the diagonals of rhombus    are perpendicular.  (2 marks)
   

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The diagram below shows a rhombus, spanned by the two vectors    and  .
 

It follows that