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×(×).

  • AUVW(×)=0, UVW×(×)=8,0,4
  • BUVW(×)=14, UVW×(×)=7,0,1
  • CUVW(×)=0, UVW×(×)=13,0,19
  • DUVW(×)=5, UVW×(×)=2,0,12
  • EUVW(×)=14, UVW×(×)=13,0,19

Q2:

Find 4,5,1×0,5,5×1,5,2.

  • A6080+130ijk
  • B12510jk
  • C3020+20ijk
  • D14080+130ijk

Q3:

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

  • A45+9ij
  • B36+72ij
  • C81+81ij
  • D3672ij

Q4:

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

  • A7070ij
  • B10+10ij
  • C60+80ij
  • D70+70ij

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×(×).

  • AUVW(×)=10, UVW×(×)=8,10,2
  • BUVW(×)=10, UVW×(×)=28,10,22
  • CUVW(×)=0, UVW×(×)=28,10,22
  • DUVW(×)=8, UVW×(×)=6,0,4
  • EUVW(×)=0, UVW×(×)=8,10,2

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.

  • A28+28ij
  • B1816ij
  • C10+12ij
  • D18+16ij

Q8:

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

  • A108ij
  • B18+12ij
  • C8+4ij
  • D1812ij

Q9:

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

  • A248ij
  • B8+4ij
  • C32+12ij
  • D24+8ij

Q10:

Find 3,3,4×4,4,1×0,5,4.

  • A52+52+65ijk
  • B60+16jk
  • C13+13ij
  • D52+52+65ijk

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