The coordinates of three points are 

1. Find    (1 mark)
   

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2. The points and are the vertices of a triangle. 
   

    

   Prove that the triangle has a right angle at   (2 marks)
   

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3. Find the length of the hypotenuse of the triangle.  (1 mark)
   

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Two vectors are given by    and  , where  , .

If    and    is perpendicular to  , then find and .   (2 marks)

Consider the three vectors

  and  , where 

1. Find the value(s) of for which    (2 marks)
2. Find the value of such that    is perpendicular to    (1 mark)