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Lesson Worksheet: Scalar Triple Product Mathematics

In this worksheet, we will practice calculating the scalar triple product and apply this in geometrical applications.


True or False: The scalar triple product of vectors is equal to the determinant of the matrix formed from these vectors.

  • ATrue
  • BFalse


Find ijkjkikij(×)+(×)+(×).


Given A=1,5,5, B=2,4,3, and C=0,5,4, find ABC(×).


Consider A=1,2,3, B=4,5,3, and C=1,2,2.

Find ABC(×).

Find BAC(×).


Given that A=1,2,4, B=2,4,1, and C=1,4,2, find ABCBCACAB(×)+(×)+(×).


If 𝑣, 𝑤, and 𝑢 are three linearly independent vectors in , then the volume of the parallelepiped determined by 𝑣, 𝑤, and 𝑢 is .

  • A|𝑣(𝑤×𝑢)|
  • B|𝑣|+|𝑤|+|𝑢|
  • C|𝑣|+|𝑤|+|𝑢|
  • D|𝑣||𝑤||𝑢|


True or False: The scalar triple product of u, v, and w results in a vector whose length is equal to the volume of the parallelepiped determined by u, v, and w.

  • AFalse
  • BTrue


Find the volume of the parallelepiped with the adjacent sides U=1,1,3, V=2,1,4, and W=5,1,2.


Find the value of 𝑘 for which the four points (1,7,2), (3,5,6), (1,6,4), and (4,3,𝑘) all lie in a single plane.


The parallelepiped on vectors 2,2,𝑚, 2,0,2, and 5,1,0 has volume 48. What can 𝑚 be?

  • A16 or 32
  • B16 or 12
  • C36 or 32
  • D36 or 12

This lesson includes 23 additional questions and 180 additional question variations for subscribers.

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