Worksheet: Vector Triple Product

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

Q1:

U , V , and W are three vectors, where U=1,0,2, V=1,0,3, and W=2,0,2. Calculate UVW(×) and UVW×(×).

  • A U V W ( × ) = 0 , U V W × ( × ) = 8 , 0 , 4
  • B U V W ( × ) = 1 4 , U V W × ( × ) = 7 , 0 , 1
  • C U V W ( × ) = 0 , U V W × ( × ) = 1 3 , 0 , 1 9
  • D U V W ( × ) = 5 , U V W × ( × ) = 2 , 0 , 1 2
  • E U V W ( × ) = 1 4 , U V W × ( × ) = 1 3 , 0 , 1 9

Q2:

Find 4,5,1×0,5,5×1,5,2.

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

Q3:

If Aij=5, Bij=63, and Cij=3+3, determine (×)×BCA.

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

Q4:

Determine ACB×(×) if Aij=5+5, Bij=4+3, and Cij=2+2.

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

Q5:

U , V , and W are three vectors, where U=1,1,1, V=3,0,2, and W=2,2,2. Calculate UVW(×) and UVW×(×).

  • A U V W ( × ) = 1 0 , U V W × ( × ) = 8 , 1 0 , 2
  • B U V W ( × ) = 1 0 , U V W × ( × ) = 2 8 , 1 0 , 2 2
  • C U V W ( × ) = 0 , U V W × ( × ) = 2 8 , 1 0 , 2 2
  • D U V W ( × ) = 8 , U V W × ( × ) = 6 , 0 , 4
  • E U V W ( × ) = 0 , U V W × ( × ) = 8 , 1 0 , 2

Q6:

Determine the volume of a parallelepiped on the vectors 𝑂𝐴, 𝑂𝐵, and 𝑂𝐶, 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 Aij=89, Bij=2+2, and Cij=6+5, determine (×)×ACB.

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

Q8:

If Aij=2, Bij=46, and Cij=45, determine (×)×BAC.

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

Q9:

Determine ABC×(×) if Aij=2+6, Bij=24, and Cij=3+8.

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

Q10:

Find 3,3,4×4,4,1×0,5,4.

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

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