Worksheet: Vector Triple Product

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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⟩.

  • A−60−80+130ijk
  • B125−10jk
  • C30−20+20ijk
  • D−140−80+130ijk

Q3:

If Aij=−−5, Bij=−6−3, and Cij=3+3, determine (×)×BCA.

  • A−45+9ij
  • B−36+72ij
  • C−81+81ij
  • D36−72ij

Q4:

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

  • A−70−70ij
  • B−10+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=8−9, Bij=−2+2, and Cij=−6+5, determine (×)×ACB.

  • A28+28ij
  • B−18−16ij
  • C10+12ij
  • D18+16ij

Q8:

If Aij=−2, Bij=4−6, and Cij=4−5, determine (×)×BAC.

  • A−10−8ij
  • B18+12ij
  • C8+4ij
  • D−18−12ij

Q9:

Determine ABC×(×) if Aij=2+6, Bij=−2−4, and Cij=3+8.

  • A24−8ij
  • B−8+4ij
  • C−32+12ij
  • D−24+8ij

Q10:

Find ⟨3,3,4⟩×⟨4,4,1⟩×⟨0,−5,4⟩.

  • A−52+52+65ijk
  • B−60+16jk
  • C−13+13ij
  • D52+52+65ijk

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