Worksheet: Vector Triple Product

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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