In a rectangular prism, is the midpoint of .

Use vector methods to find

1. to 1 decimal place  (2 marks)
   

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2. to 1 decimal place  (2 marks)
   

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Four cubes are placed in a line as shown on the diagram.
 

Which of the following vectors is equal to

A cube with side length 3 units is pictured below.
 

1. Calculate the magnitude of vector .  (1 mark)
   

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2. Find the acute angle between the diagonals and .  (3 marks)
   

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are the vertices of a rectangular prism.
  

1. Show that the internal diagonals of the prism, and , intersect.  (2 marks)
   

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2. Calculate the acute angle, , between the diagonals, to the nearest minute.  (2 marks)
   

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