Points and form a triangle in the Cartesian Plane.

1. Find the vectors and .    (1 mark)
   

   --- 2 WORK AREA LINES (style=lined) ---

2. Find the angle  ,  giving your answer to the nearest degree.     (2 marks)
   

   --- 5 WORK AREA LINES (style=lined) ---

A parallelogram is formed by joining the points  and .

Use vector methods to find and .   (2 marks)

In the diagram, is a parallelogram. where    and  .
 

Given is the midpoint of , determine which expression represents vector .

  is a quadrilateral.

, , and divide each side of the quadrilateral in half as shown below.
  

Prove, using vectors, that    is a parallelogram.  (3 marks)

  is a parallelogram, where    and 
 

Prove, using vectors, that the sum of the squares of the lengths of the diagonals is equal to the sum of the squares of the lengths of the sides.  (3 marks)