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Vectors, EXT2 V1 2020 HSC 15b

The point divides the interval so that  . The position vectors of and are and respectively, as shown in the diagram.
 

  1. Show that  .  (2 marks)

     

  2. Prove that  .  (1 mark)

Let be a parallelogram with    and  . The point is the midpoint of and is the intersection of and , as shown in the diagram.
  
 
         
 

  1. Show that  .  (3 marks)

  2. Using parts (ii) and (iii), or otherwise, prove that is the point that divides the interval in the ratio 2 :1.   (1 mark)

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i.  

 

 

ii.   
   
   
   
   
   

 

iii. 

♦ Mean mark part (iii) 50%.
 

 


 

 
 
Mean mark part (iv) 51%.

 

iv.   

 

 

Vectors, EXT2 V1 2019 SPEC2 4

The base of a pyramid is the parallelogram    with vertices at points    and  . The apex (top) of the pyramid is located at  .

  1. Find the values of    and  .  (2 marks)

  2. Find the cosine of the angle between the vectors    and  .  (2 marks)

  3. Find the area of the base of the pyramid.  (2 marks)

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  3. ²
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i.   
   

 

 

ii.   

 
 

 

iii.   
 

  

  

  ²

Vectors, EXT2 V1 2015 VCE 1

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

VCAA 2015 spec 1a
 

  1. Find    (1 mark)

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

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i.   

 

 

ii.   

MARKER’S COMMENT: Vector notation was poor in many answers.