Lesson Worksheet: Vector Triple Product Mathematics

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


Find 4,5,1×0,5,5×1,5,2.

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


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

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


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

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


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.


True or False: (×)×=×(×)abccab.

  • AFalse
  • BTrue


True or False: abcacbabc×(×)=()().

  • AFalse
  • BTrue


True or False: The geometric meaning of the vector triple product abc×(×) is the volume of the parallelepiped defined by the three vectors a, b, and c.

  • ATrue
  • BFalse


True or False: If (×)×(×)=abcd0, then the plane that contains a and b and the plane that contains c and d are parallel planes.

  • ATrue
  • BFalse

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