Lesson: Vector Triple Product

In this lesson, we will learn how to calculate the triple vector product of three vectors.

Sample Question Videos

  • 07:30

Worksheet: 10 Questions • 1 Video

Q1:

U , V , and W are three vectors, where U = 1 , 0 , 2 , V = 1 , 0 , 3 , and W = 2 , 0 , 2 . Calculate U V W ( × ) and U V W × ( × ) .

Q2:

Find 4 , 5 , 1 × 0 , 5 , 5 × 1 , 5 , 2 .

Q3:

If 𝐴 = 𝑖 5 𝑗 , 𝐵 = 6 𝑖 3 𝑗 , and 𝐶 = 3 𝑖 + 3 𝑗 , determine ( 𝐵 × 𝐶 ) × 𝐴 .

Q4:

Determine 𝐴 × ( 𝐶 × 𝐵 ) if 𝐴 = 5 𝑖 + 5 𝑗 , 𝐵 = 4 𝑖 + 3 𝑗 , and 𝐶 = 2 𝑖 + 2 𝑗 .

Q5:

U , V , and W are three vectors, where U = 1 , 1 , 1 , V = 3 , 0 , 2 , and W = 2 , 2 , 2 . Calculate U V W ( × ) and U V W × ( × ) .

Q6:

Determine the volume of a parallelepiped on the vectors 𝑂 𝐴 , 𝑂 𝐵 , and 𝑂 𝐶 , 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 𝐴 = 8 𝑖 9 𝑗 , 𝐵 = 2 𝑖 + 2 𝑗 , and 𝐶 = 6 𝑖 + 5 𝑗 , determine ( 𝐴 × 𝐶 ) × 𝐵 .

Q8:

If 𝐴 = 𝑖 2 𝑗 , 𝐵 = 4 𝑖 6 𝑗 , and 𝐶 = 4 𝑖 5 𝑗 , determine ( 𝐵 × 𝐴 ) × 𝐶 .

Q9:

Determine 𝐴 × ( 𝐵 × 𝐶 ) if 𝐴 = 2 𝑖 + 6 𝑗 , 𝐵 = 2 𝑖 4 𝑗 , and 𝐶 = 3 𝑖 + 8 𝑗 .

Q10:

Find 3 , 3 , 4 × 4 , 4 , 1 × 0 , 5 , 4 .

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