# Lesson Worksheet: Scalar Triple Product Mathematics

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

Q1:

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

• ATrue
• BFalse

Q2:

Find .

Q3:

Given , , and , find .

Q4:

Consider , , and .

Find .

Find .

Q5:

Given that , , and , find .

Q6:

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

• A
• B
• C
• D

Q7:

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

• ATrue
• BFalse

Q8:

Find the volume of the parallelepiped with the adjacent sides , , and .

Q9:

Find the value of for which the four points , , , and all lie in a single plane.

Q10:

The parallelepiped on vectors , , and has volume 48. What can be?

• A16 or
• B16 or
• C36 or
• D36 or