Worksheet: Scalar Triple Product

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

Q1:

If A=3,0,2, B=1,3,3, and C=2,2,1, find (+)[(×)×(×)]ACABBC.

Q2:

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

Q3:

Find ijkjkikij(×)+(×)+(×).

Q4:

If Aij=2+, Bij=24, and Cij=9+3, calculate (×)ACB.

Q5:

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

Q6:

If Aij=3+7, Bij=22, and Cij=4, calculate ()×BCA.

Q7:

Find the volume of the parallelepiped in which three adjacent sides are represented by the vectors A=3,2,5, B=1,7,8, and C=7,2,5.

Q8:

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

Q9:

Find the volume of the parallelepiped with the adjacent sides U=1,3,2, V=7,2,10, and W=1,0,1.

Q10:

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|

Q11:

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.

Q12:

Suppose that vectors (3,4,5), (1,2,3), and (3,𝑘,3) are all in the same plane. What is the value of 𝑘?

Q13:

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

Q14:

If Aij=55, Bij=+, and Cij=85, calculate (×)CBA.

Q15:

If Aij=2+5, Bij=+2, and Cij=4+9, calculate (×)BAC.

Q16:

If Aij=3, Bij=3+2, and Cij=8+8, calculate (×)BCA.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.