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Lesson: Scalar Triple Product

Sample Question Videos

Worksheet • 16 Questions • 1 Video

Q1:

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

Q2:

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

Q3:

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

Q4:

Find 𝑖 𝑗 × 𝑘 + 𝑗 𝑘 × 𝑖 + 𝑘 𝑖 × 𝑗 .

Q5:

If 𝐴 = 2 𝑖 + 𝑗 , 𝐵 = 2 𝑖 4 𝑗 , and 𝐶 = 9 𝑖 + 3 𝑗 , calculate ( 𝐴 × 𝐶 ) 𝐵 .

  • A0
  • B 3 0 𝑘
  • C 3 0 𝑖 + 6 0 𝑗
  • D 1 8 𝑖 5 4 𝑗
  • E 3 0 𝑖 6 0 𝑗

Q6:

If 𝐴 = 5 𝑖 5 𝑗 , 𝐵 = 𝑖 + 𝑗 , and 𝐶 = 8 𝑖 5 𝑗 , calculate ( 𝐶 × 𝐵 ) 𝐴 .

  • A0
  • B 3 0 𝑘
  • C 5 0 𝑖 + 8 0 𝑗
  • D 1 5 𝑖 1 5 𝑗
  • E 5 0 𝑖 8 0 𝑗

Q7:

If 𝐴 = 2 𝑖 + 5 𝑗 , 𝐵 = 𝑖 + 2 𝑗 , and 𝐶 = 4 𝑖 + 9 𝑗 , calculate ( 𝐵 × 𝐴 ) 𝐶 .

  • A0
  • B 3 8 𝑘
  • C 7 6 𝑖 3 8 𝑗
  • D 8 5 𝑖 + 3 4 𝑗
  • E 7 6 𝑖 + 3 8 𝑗

Q8:

If 𝐴 = 3 𝑖 𝑗 , 𝐵 = 3 𝑖 + 2 𝑗 , and 𝐶 = 8 𝑖 + 8 𝑗 , calculate ( 𝐵 × 𝐶 ) 𝐴 .

  • A0
  • B 3 2 𝑘
  • C 6 4 𝑖 9 6 𝑗
  • D 2 4 𝑖 2 4 𝑗
  • E 6 4 𝑖 + 9 6 𝑗

Q9:

If 𝐴 = 3 𝑖 + 7 𝑗 , 𝐵 = 2 𝑖 2 𝑗 , and 𝐶 = 𝑖 4 𝑗 , calculate ( 𝐵 𝐶 ) × 𝐴 .

Q10:

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

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:

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

Q13:

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 |

Q14:

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 ) .

Q15:

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

  • A36 or 1 2
  • B36 or 3 2
  • C16 or 3 2
  • D16 or 1 2

Q16:

The parallelepiped on vectors 1 , 1 , 𝑚 , 4 , 5 , 4 , and 1 , 1 , 3 has volume 17. What can 𝑚 be?

  • A 1 4 or 20
  • B 1 4 or 36
  • C2 or 36
  • D2 or 20
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