# Worksheet: Products of Vectors

In this worksheet, we will practice calculating the vector product of two vectors and using the vector product to find the angle between two vectors.

Q1:

Calculate the product . • A
• B
• C
• D
• E

Q2:

For the vectors shown in the accompanying diagram, the positive -axis corresponds to horizontally right and the positive -axis corresponds to vertically upward. Find the component of vector along vector .

Find the component of vector along vector .

Find the component of vector along vector .

Find the component of vector along vector .

Q3:

Consider the vectors and .

Find .

• A
• B
• C
• D
• E

Find .

Find the angle between and .

Find the angle between and .

Q4:

A convoy of vehicles has a velocity vector .

What is the unit vector of the convoy’s direction of motion?

• A
• B
• C
• D
• E

At what angle north of east does the convoy move?

Q5:

The positive is horizontal to the right for the vectors shown. What is the vector product ?

• A
• B
• C
• D
• E

What is the vector product ?

• A
• B
• C
• D
• E

What is the vector product ?

• A
• B
• C
• D
• E

What is the vector product ?

• A
• B
• C
• D
• E

What is the vector product ?

• A
• B
• C
• D
• E

What is the vector product ?

• A
• B
• C
• D
• E

What is the vector product ?

• A
• B
• C
• D
• E

Q6:

Calculate the product . • A
• B
• C
• D
• E

Q7:

Three dogs pull on a stick, all in different directions, exerting forces , , and . N, N, and N. The forces , , and apply the displacement vector cm to the stick.

What is the angle between and ?

What magnitude of work is done by ?

What magnitude of work is done by ?

Q8:

Calculate the product . Q9:

Calculate the product . • A
• B57.3
• C
• D71.7
• E37.5

Q10:

Find the angle between the two vectors and .

Q11:

What is the relationship between the directions of two vectors for which the dot product is zero?

• AThey are perpendicular (orthogonal).
• BThey are antiparallel.
• CThey form a 45 degrees angle with respect to one another.
• DThey are coplanar.
• EThey are parallel.

Q12:

Calculate the dot product of and . Which of the following matches the result?

• A44
• B12
• C72
• D38
• E16

Q13:

Calculate the cross product of and . Which of the following best matches the result?

• A
• B
• C
• D
• E

Q14:

Which of the following is closest to the angle between the two vectors and ?

• A70 degrees
• B32 degrees
• C55 degrees
• D5 degrees
• E50 degrees

Q15:

Two displacement vectors and have magnitudes of 10.0 m and 20.0 m respectively. The directions of and make counterclockwise angles of and ,respectively, with the positive , as shown in the accompanying diagram. Find the product . Answer to three significant figures. 