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Vectors, SPEC1 2023 VCAA 9

A plane contains the points and , where is a real constant. The plane has a -axis intercept of 2 at the point .

  1. Write down the coordinates of point .   (1 mark)
  1. Show that and are   and  , respectively.   (1 mark)
  1. Hence find the equation of the plane in Cartesian form.  (2 marks)
  1.  Find .   (1 mark)
  1.   and are adjacent sides of a parallelogram. Find the area of this parallelogram.   (1 mark)
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a.   

b.   

c.   

d.   

e.   

Show Worked Solution

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b.   

 
c.   

 
d.   

e.    
   
   
   

Vectors, SPEC1 2015 VCAA 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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a.   

 

 

b.   

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