Worksheet: Vector Triple Product

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In this worksheet, we will practice calculating the triple product vectors.

Q1:

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

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

Q2:

Find ( − 4 , − 5 , 1 ) × ( 0 , − 5 , − 5 ) × ( − 1 , 5 , 2 ) .

  • A 3 0 ⃑ 𝑖 − 2 0 ⃑ 𝑗 + 2 0 ⃑ 𝑘
  • B − 6 0 ⃑ 𝑖 − 8 0 ⃑ 𝑗 + 1 3 0 ⃑ 𝑘
  • C 1 2 5 ⃑ 𝑗 − 1 0 ⃑ 𝑘
  • D − 1 4 0 ⃑ 𝑖 − 8 0 ⃑ 𝑗 + 1 3 0 ⃑ 𝑘

Q3:

If ⃑ 𝐴 = − ⃑ 𝑖 − 5 ⃑ 𝑗 , ⃑ 𝐵 = − 6 ⃑ 𝑖 − 3 ⃑ 𝑗 , and ⃑ 𝐶 = 3 ⃑ 𝑖 + 3 ⃑ 𝑗 , determine ( ⃑ 𝐵 × ⃑ 𝐶 ) × ⃑ 𝐴 .

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

Q4:

Determine ⃑ 𝐴 × ( ⃑ 𝐶 × ⃑ 𝐵 ) if ⃑ 𝐴 = − 5 ⃑ 𝑖 + 5 ⃑ 𝑗 , ⃑ 𝐵 = − 4 ⃑ 𝑖 + 3 ⃑ 𝑗 , and ⃑ 𝐶 = 2 ⃑ 𝑖 + 2 ⃑ 𝑗 .

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

Q5:

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

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

Q6:

Determine the volume of a parallelepiped on the vectors 𝑂 𝐴 , 𝑂 𝐵 , and 𝑂 𝐶 , given that the coordinates of points 𝑂 , 𝐴 , 𝐵 , and 𝐶 are ( 3 , 5 , 3 ) , ( − 4 , 0 , − 2 ) , ( − 2 , − 4 , 0 ) , and ( 0 , 5 , 3 ) , respectively.

Q7:

If ⃑ 𝐴 = 8 ⃑ 𝑖 − 9 ⃑ 𝑗 , ⃑ 𝐵 = − 2 ⃑ 𝑖 + 2 ⃑ 𝑗 , and ⃑ 𝐶 = − 6 ⃑ 𝑖 + 5 ⃑ 𝑗 , determine ( ⃑ 𝐴 × ⃑ 𝐶 ) × ⃑ 𝐵 .

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

Q8:

If ⃑ 𝐴 = ⃑ 𝑖 − 2 ⃑ 𝑗 , ⃑ 𝐵 = 4 ⃑ 𝑖 − 6 ⃑ 𝑗 , and ⃑ 𝐶 = 4 ⃑ 𝑖 − 5 ⃑ 𝑗 , determine ( ⃑ 𝐵 × ⃑ 𝐴 ) × ⃑ 𝐶 .

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

Q9:

Determine ⃑ 𝐴 × ( ⃑ 𝐵 × ⃑ 𝐶 ) if ⃑ 𝐴 = 2 ⃑ 𝑖 + 6 ⃑ 𝑗 , ⃑ 𝐵 = − 2 ⃑ 𝑖 − 4 ⃑ 𝑗 , and ⃑ 𝐶 = 3 ⃑ 𝑖 + 8 ⃑ 𝑗 .

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

Q10:

Find ( 3 , 3 , 4 ) × ( 4 , 4 , 1 ) × ( 0 , − 5 , 4 ) .

  • A − 1 3 ⃑ 𝑖 + 1 3 ⃑ 𝑗
  • B − 5 2 ⃑ 𝑖 + 5 2 ⃑ 𝑗 + 6 5 ⃑ 𝑘
  • C − 6 0 ⃑ 𝑗 + 1 6 ⃑ 𝑘
  • D 5 2 ⃑ 𝑖 + 5 2 ⃑ 𝑗 + 6 5 ⃑ 𝑘

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