Worksheet: Position Vectors in 2D or 3D

In this worksheet, we will practice determining the position vector of a point in two or three dimensions.

Q1:

A particle started moving along a straight line. At time 𝑡 (where 𝑡 0 ), its position relative to a fixed point is given by Determine all the possible value of 𝑡 at which 𝑟 = 4 .

  • A 1 2 , 3
  • B 2 , 3
  • C 3 2
  • D1
  • E2

Q2:

Using point ( 4 , 9 , 9 ) and direction vector 5 , 1 , 6 , give the position vector r of the point on this line corresponding to parameter 𝑡 = 9 .

  • A r = 4 9 , 0 , 4 5
  • B r = 4 9 , 0 , 4 5
  • C r = 4 , 9 , 9
  • D r = 4 1 , 1 8 , 6 3

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