Worksheet: Directed Line Segments

In this worksheet, we will practice expressing a directed line segment in terms of the coordinates of its terminals.

Q1:

The vector describes a translation from point to point .

What is another way of writing the vector ?

  • A
  • B
  • C
  • D
  • E

Q2:

For the points 𝑃 = ( 1 , 1 , 1 ) , 𝑄 = ( 2 , 2 , 2 ) , 𝑅 = ( 2 , 0 , 1 ) , and 𝑆 = ( 3 , 1 , 2 ) , is 𝑃 𝑄 = 𝑅 𝑆 ?

  • Ayes
  • Bno

Q3:

What is the terminal point of the vector 𝐴 𝐵 ?

  • A 𝐴 𝐵
  • B 𝐴
  • C 𝐴 + 𝐵
  • D 𝐵
  • E 𝐵 𝐴

Q4:

For the points 𝑃 = ( 0 , 0 , 0 ) , 𝑄 = ( 1 , 3 , 2 ) , 𝑅 = ( 1 , 0 , 1 ) , and 𝑆 = ( 2 , 3 , 4 ) , is 𝑃 𝑄 = 𝑅 𝑆 ?

  • Ano
  • Byes

Q5:

Given points 𝐴 = ( 5 , 2 , 2 ) , and 𝐵 = ( 8 , 9 , 5 ) , find 𝐴 𝐵 and 𝐵 𝐴 .

  • A 𝐴 𝐵 = ( 1 3 , 1 1 , 3 ) , 𝐵 𝐴 = ( 3 , 7 , 7 )
  • B 𝐴 𝐵 = ( 3 , 7 , 7 ) , 𝐵 𝐴 = ( 3 , 7 , 7 )
  • C 𝐴 𝐵 = ( 3 , 7 , 7 ) , 𝐵 𝐴 = ( 6 , 5 , 1 )
  • D 𝐴 𝐵 = ( 3 , 7 , 7 ) , 𝐵 𝐴 = ( 3 , 7 , 7 )

Q6:

Given 𝐴 𝐵 = ( 1 , 3 , 0 ) and 𝐴 = ( 4 , 5 , 5 ) , express 𝐵 in terms of the fundamental unit vectors.

  • A 3 𝑖 2 𝑗 5 𝑘
  • B 3 𝑖 + 2 𝑗 + 5 𝑘
  • C 5 𝑖 + 8 𝑗 + 5 𝑘
  • D 5 𝑖 8 𝑗 5 𝑘

Q7:

The coordinates of 𝐴 and 𝐵 are ( 1 , 5 , 2 ) and ( 0 , 4 , 2 ) respectively. If 𝐶 is the midpoint of 𝐴 𝐵 , what is 𝐵 𝐶 ?

  • A 1 , 1 , 4
  • B 1 2 , 1 2 , 2
  • C 1 , 1 , 4
  • D 1 2 , 1 2 , 2

Q8:

Given points 𝐴 = ( 1 , 6 , 7 ) , and 𝐵 = ( 1 , 7 , 2 ) , find 𝐴 𝐵 and 𝐵 𝐴 .

  • A 𝐴 𝐵 = ( 2 , 1 , 9 ) , 𝐵 𝐴 = ( 0 , 1 3 , 5 )
  • B 𝐴 𝐵 = ( 0 , 1 3 , 5 ) , 𝐵 𝐴 = ( 0 , 1 3 , 5 )
  • C 𝐴 𝐵 = ( 0 , 1 3 , 5 ) , 𝐵 𝐴 = ( 1 , 0 , 4 )
  • D 𝐴 𝐵 = ( 0 , 1 3 , 5 ) , 𝐵 𝐴 = ( 0 , 1 3 , 5 )

Q9:

Given points 𝐴 = ( 9 , 9 , 6 ) , and 𝐵 = ( 6 , 8 , 4 ) , find 𝐴 𝐵 and 𝐵 𝐴 .

  • A 𝐴 𝐵 = ( 1 5 , 1 7 , 2 ) , 𝐵 𝐴 = ( 3 , 1 , 1 0 )
  • B 𝐴 𝐵 = ( 3 , 1 , 1 0 ) , 𝐵 𝐴 = ( 3 , 1 , 1 0 )
  • C 𝐴 𝐵 = ( 3 , 1 , 1 0 ) , 𝐵 𝐴 = ( 7 , 8 , 1 )
  • D 𝐴 𝐵 = ( 3 , 1 , 1 0 ) , 𝐵 𝐴 = ( 3 , 1 , 1 0 )

Q10:

The coordinates of 𝐴 and 𝐵 are ( 4 , 4 , 5 ) and ( 4 , 0 , 4 ) respectively. If 𝐶 is the midpoint of 𝐴 𝐵 , what is 𝐵 𝐶 ?

  • A 8 , 4 , 9
  • B 4 , 2 , 9 2
  • C 8 , 4 , 9
  • D 4 , 2 , 9 2

Q11:

The coordinates of 𝐴 and 𝐵 are ( 1 , 5 , 2 ) and ( 4 , 2 , 0 ) respectively. If 𝐶 is the midpoint of 𝐴 𝐵 , what is 𝐵 𝐶 ?

  • A 5 , 7 , 2
  • B 5 2 , 7 2 , 1
  • C 5 , 7 , 2
  • D 5 2 , 7 2 , 1

Q12:

Given 𝐴 𝐵 = ( 2 , 4 , 3 ) and 𝐴 = ( 3 , 1 , 2 ) , express 𝐵 in terms of the fundamental unit vectors.

  • A 5 𝑖 3 𝑗 𝑘
  • B 5 𝑖 + 3 𝑗 + 𝑘
  • C 𝑖 5 𝑗 5 𝑘
  • D 𝑖 + 5 𝑗 + 5 𝑘

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