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Worksheet: Directed Line Segments

Q1:

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

  • Ano
  • Byes

Q2:

The vector u describes a translation from point 𝐴 to point 𝐡 .

What is another way of writing the vector u ?

  • A οƒ  𝐡 𝐴
  • B βˆ’ οƒ  𝐴 𝐡
  • C A
  • D οƒ  𝐴 𝐡
  • E B

Q3:

Given two points , and , determine and .

  • A ,
  • B ,
  • C ,
  • D ,

Q4:

Given two points , and , determine and .

  • A ,
  • B ,
  • C ,
  • D ,

Q5:

Given two points , and , determine and .

  • A ,
  • B ,
  • C ,
  • D ,

Q6:

The coordinates of 𝐴 and 𝐡 are ( 1 , βˆ’ 5 , 2 ) and ( 0 , βˆ’ 4 , βˆ’ 2 ) respectively. If 𝐢 is the midpoint of 𝐴 𝐡 , what is οƒŸ 𝐡 𝐢 ?

  • A ⟨ βˆ’ 1 , 1 , βˆ’ 4 ⟩
  • B  βˆ’ 1 2 , 1 2 , βˆ’ 2 ο‡·
  • C ⟨ 1 , βˆ’ 1 , 4 ⟩
  • D  1 2 , βˆ’ 1 2 , 2 ο‡·

Q7:

The coordinates of 𝐴 and 𝐡 are ( βˆ’ 4 , 4 , 5 ) and ( 4 , 0 , βˆ’ 4 ) respectively. If 𝐢 is the midpoint of 𝐴 𝐡 , what is οƒŸ 𝐡 𝐢 ?

  • A ⟨ 8 , βˆ’ 4 , βˆ’ 9 ⟩
  • B  4 , βˆ’ 2 , βˆ’ 9 2 ο‡·
  • C ⟨ βˆ’ 8 , 4 , 9 ⟩
  • D  βˆ’ 4 , 2 , 9 2 ο‡·

Q8:

The coordinates of 𝐴 and 𝐡 are ( 1 , 5 , βˆ’ 2 ) and ( βˆ’ 4 , βˆ’ 2 , 0 ) respectively. If 𝐢 is the midpoint of 𝐴 𝐡 , what is οƒŸ 𝐡 𝐢 ?

  • A ⟨ βˆ’ 5 , βˆ’ 7 , 2 ⟩
  • B  βˆ’ 5 2 , βˆ’ 7 2 , 1 ο‡·
  • C ⟨ 5 , 7 , βˆ’ 2 ⟩
  • D  5 2 , 7 2 , βˆ’ 1 ο‡·

Q9:

What is the terminal point of the vector οƒ  𝐴 𝐡 ?

  • A 𝐴 βˆ’ 𝐡
  • B 𝐴
  • C 𝐴 + 𝐡
  • D 𝐡
  • E 𝐡 βˆ’ 𝐴

Q10:

Given and , express in terms of the fundamental unit vectors.

  • A
  • B
  • C
  • D

Q11:

Given and , express in terms of the fundamental unit vectors.

  • A
  • B
  • C
  • D

Q12:

Given and , express in terms of the fundamental unit vectors.

  • A
  • B
  • C
  • D