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Lesson: Vector Triple Product

Sample Question Videos

Worksheet • 10 Questions • 1 Video

Q1:

, , and are three vectors, where , , and . Calculate and .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q2:

If ⃑ 𝐴 = βˆ’ ⃑ 𝑖 βˆ’ 5 ⃑ 𝑗 , ⃑ 𝐡 = βˆ’ 6 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 , and ⃑ 𝐢 = 3 ⃑ 𝑖 + 3 ⃑ 𝑗 , determine ( ⃑ 𝐡 Γ— ⃑ 𝐢 ) Γ— ⃑ 𝐴 .

  • A βˆ’ 4 5 ⃑ 𝑖 + 9 ⃑ 𝑗
  • B 3 6 ⃑ 𝑖 βˆ’ 7 2 ⃑ 𝑗
  • C βˆ’ 8 1 ⃑ 𝑖 + 8 1 ⃑ 𝑗
  • D βˆ’ 3 6 ⃑ 𝑖 + 7 2 ⃑ 𝑗

Q3:

If ⃑ 𝐴 = 8 ⃑ 𝑖 βˆ’ 9 ⃑ 𝑗 , ⃑ 𝐡 = βˆ’ 2 ⃑ 𝑖 + 2 ⃑ 𝑗 , and ⃑ 𝐢 = βˆ’ 6 ⃑ 𝑖 + 5 ⃑ 𝑗 , determine ( ⃑ 𝐴 Γ— ⃑ 𝐢 ) Γ— ⃑ 𝐡 .

  • A 2 8 ⃑ 𝑖 + 2 8 ⃑ 𝑗
  • B 1 8 ⃑ 𝑖 + 1 6 ⃑ 𝑗
  • C 1 0 ⃑ 𝑖 + 1 2 ⃑ 𝑗
  • D βˆ’ 1 8 ⃑ 𝑖 βˆ’ 1 6 ⃑ 𝑗

Q4:

If ⃑ 𝐴 = ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 , ⃑ 𝐡 = 4 ⃑ 𝑖 βˆ’ 6 ⃑ 𝑗 , and ⃑ 𝐢 = 4 ⃑ 𝑖 βˆ’ 5 ⃑ 𝑗 , determine ( ⃑ 𝐡 Γ— ⃑ 𝐴 ) Γ— ⃑ 𝐢 .

  • A βˆ’ 1 0 ⃑ 𝑖 βˆ’ 8 ⃑ 𝑗
  • B βˆ’ 1 8 ⃑ 𝑖 βˆ’ 1 2 ⃑ 𝑗
  • C 8 ⃑ 𝑖 + 4 ⃑ 𝑗
  • D 1 8 ⃑ 𝑖 + 1 2 ⃑ 𝑗

Q5:

Determine ⃑ 𝐴 Γ— ( ⃑ 𝐢 Γ— ⃑ 𝐡 ) if ⃑ 𝐴 = βˆ’ 5 ⃑ 𝑖 + 5 ⃑ 𝑗 , ⃑ 𝐡 = βˆ’ 4 ⃑ 𝑖 + 3 ⃑ 𝑗 , and ⃑ 𝐢 = 2 ⃑ 𝑖 + 2 ⃑ 𝑗 .

  • A 7 0 ⃑ 𝑖 + 7 0 ⃑ 𝑗
  • B 6 0 ⃑ 𝑖 + 8 0 ⃑ 𝑗
  • C βˆ’ 1 0 ⃑ 𝑖 + 1 0 ⃑ 𝑗
  • D βˆ’ 7 0 ⃑ 𝑖 βˆ’ 7 0 ⃑ 𝑗

Q6:

Determine ⃑ 𝐴 Γ— ( ⃑ 𝐡 Γ— ⃑ 𝐢 ) if ⃑ 𝐴 = 2 ⃑ 𝑖 + 6 ⃑ 𝑗 , ⃑ 𝐡 = βˆ’ 2 ⃑ 𝑖 βˆ’ 4 ⃑ 𝑗 , and ⃑ 𝐢 = 3 ⃑ 𝑖 + 8 ⃑ 𝑗 .

  • A βˆ’ 2 4 ⃑ 𝑖 + 8 ⃑ 𝑗
  • B βˆ’ 3 2 ⃑ 𝑖 + 1 2 ⃑ 𝑗
  • C βˆ’ 8 ⃑ 𝑖 + 4 ⃑ 𝑗
  • D 2 4 ⃑ 𝑖 βˆ’ 8 ⃑ 𝑗

Q7:

Find ( βˆ’ 4 , βˆ’ 5 , 1 ) Γ— ( 0 , βˆ’ 5 , βˆ’ 5 ) Γ— ( βˆ’ 1 , 5 , 2 ) .

  • A βˆ’ 1 4 0 ⃑ 𝑖 βˆ’ 8 0 ⃑ 𝑗 + 1 3 0 ⃑ π‘˜
  • B βˆ’ 6 0 ⃑ 𝑖 βˆ’ 8 0 ⃑ 𝑗 + 1 3 0 ⃑ π‘˜
  • C 1 2 5 ⃑ 𝑗 βˆ’ 1 0 ⃑ π‘˜
  • D 3 0 ⃑ 𝑖 βˆ’ 2 0 ⃑ 𝑗 + 2 0 ⃑ π‘˜

Q8:

Find ( 3 , 3 , 4 ) Γ— ( 4 , 4 , 1 ) Γ— ( 0 , βˆ’ 5 , 4 ) .

  • A 5 2 ⃑ 𝑖 + 5 2 ⃑ 𝑗 + 6 5 ⃑ π‘˜
  • B βˆ’ 5 2 ⃑ 𝑖 + 5 2 ⃑ 𝑗 + 6 5 ⃑ π‘˜
  • C βˆ’ 6 0 ⃑ 𝑗 + 1 6 ⃑ π‘˜
  • D βˆ’ 1 3 ⃑ 𝑖 + 1 3 ⃑ 𝑗

Q9:

Find ( βˆ’ 1 , βˆ’ 4 , 1 ) Γ— ( βˆ’ 2 , 5 , 4 ) Γ— ( 5 , βˆ’ 4 , 4 ) .

  • A βˆ’ 4 4 ⃑ 𝑖 + 1 9 ⃑ 𝑗 + 7 4 ⃑ π‘˜
  • B βˆ’ 6 0 ⃑ 𝑖 + 1 9 ⃑ 𝑗 + 7 4 ⃑ π‘˜
  • C 1 0 ⃑ 𝑖 + 8 0 ⃑ 𝑗 + 1 6 ⃑ π‘˜
  • D βˆ’ 2 1 ⃑ 𝑖 + 2 ⃑ 𝑗 βˆ’ 1 3 ⃑ π‘˜

Q10:

Find ( 1 , βˆ’ 1 , βˆ’ 2 ) Γ— ( βˆ’ 4 , 5 , 0 ) Γ— ( βˆ’ 4 , 1 , βˆ’ 3 ) .

  • A βˆ’ 2 5 ⃑ 𝑖 + 2 6 ⃑ 𝑗 + 4 2 ⃑ π‘˜
  • B 2 3 ⃑ 𝑖 + 2 6 ⃑ 𝑗 + 4 2 ⃑ π‘˜
  • C 1 6 ⃑ 𝑖 βˆ’ 5 ⃑ 𝑗
  • D 1 0 ⃑ 𝑖 + 8 ⃑ 𝑗 + ⃑ π‘˜
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