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Vectors, SPEC1 2024 VCAA 4

Consider the vectors    and  ,  where  .

  1. Find the angle between and .   (2 marks)

  2. Find all possible values of such that the dot product of and is equal to the magnitude of the cross product of and .   (2 marks)

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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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