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Lesson: Directed Line Segments

Worksheet • 12 Questions

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 ?

  • Ayes
  • Bno

Q2:

The vector describes a translation from point to point .

What is another way of writing the vector ?

  • A
  • B
  • C
  • D
  • E

Q3:

Given points 𝐴 = ( βˆ’ 5 , 2 , βˆ’ 2 ) , and 𝐡 = ( βˆ’ 8 , 9 , 5 ) , find οƒ  𝐴 𝐡 and οƒ  𝐡 𝐴 .

  • A οƒ  𝐴 𝐡 = ( βˆ’ 3 , 7 , 7 ) , οƒ  𝐡 𝐴 = ( 3 , βˆ’ 7 , βˆ’ 7 )
  • B οƒ  𝐴 𝐡 = ( 3 , βˆ’ 7 , βˆ’ 7 ) , οƒ  𝐡 𝐴 = ( βˆ’ 3 , 7 , 7 )
  • C οƒ  𝐴 𝐡 = ( βˆ’ 3 , 7 , 7 ) , οƒ  𝐡 𝐴 = ( βˆ’ 6 , 5 , 1 )
  • D οƒ  𝐴 𝐡 = ( βˆ’ 1 3 , 1 1 , 3 ) , οƒ  𝐡 𝐴 = ( 3 , βˆ’ 7 , βˆ’ 7 )

Q4:

Given points 𝐴 = ( βˆ’ 1 , 6 , βˆ’ 7 ) , and 𝐡 = ( βˆ’ 1 , βˆ’ 7 , βˆ’ 2 ) , find οƒ  𝐴 𝐡 and οƒ  𝐡 𝐴 .

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

Q5:

Given points 𝐴 = ( 9 , 9 , 6 ) , and 𝐡 = ( 6 , 8 , βˆ’ 4 ) , find οƒ  𝐴 𝐡 and οƒ  𝐡 𝐴 .

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

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

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

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

Q9:

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

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

Q10:

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

  • A βˆ’ 5 ⃑ 𝑖 βˆ’ 8 ⃑ 𝑗 βˆ’ 5 ⃑ π‘˜
  • B 3 ⃑ 𝑖 + 2 ⃑ 𝑗 + 5 ⃑ π‘˜
  • C 5 ⃑ 𝑖 + 8 ⃑ 𝑗 + 5 ⃑ π‘˜
  • D βˆ’ 3 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 βˆ’ 5 ⃑ π‘˜

Q11:

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

  • A βˆ’ ⃑ 𝑖 + 5 ⃑ 𝑗 + 5 ⃑ π‘˜
  • B 5 ⃑ 𝑖 + 3 ⃑ 𝑗 + ⃑ π‘˜
  • C ⃑ 𝑖 βˆ’ 5 ⃑ 𝑗 βˆ’ 5 ⃑ π‘˜
  • D βˆ’ 5 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 βˆ’ ⃑ π‘˜

Q12:

Given οƒ  𝐴 𝐡 = ( 2 , βˆ’ 4 , βˆ’ 1 ) and ⃑ 𝐴 = ( 3 , 1 , 0 ) , express ⃑ 𝐡 in terms of the fundamental unit vectors.

  • A 5 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 βˆ’ ⃑ π‘˜
  • B βˆ’ ⃑ 𝑖 βˆ’ 5 ⃑ 𝑗 βˆ’ ⃑ π‘˜
  • C βˆ’ 5 ⃑ 𝑖 + 3 ⃑ 𝑗 + ⃑ π‘˜
  • D ⃑ 𝑖 + 5 ⃑ 𝑗 + ⃑ π‘˜
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