# 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 upwards.

Find the component of vector along vector .

• A7.13
• B6.46
• C8.49
• D8.66
• E9.12

Find the component of vector along vector .

• A10.4
• B11.0
• C9.35
• D8.73
• E10.1

Find the component of vector along vector .

• A0.909
• B0.708
• C0.866
• D0.783
• E0.810

Find the component of vector along vector .

• A17.3
• B18.0
• C16.8
• D13.8
• E15.1

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 -axis 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 .

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

Q12:

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

• A16
• B12
• C72
• D44
• E38

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 ?

• A 70 degrees
• B 55 degrees
• C 32 degrees
• D 50 degrees
• E 5 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 -axis, as shown in the accompanying diagram. Find the product . Answer to three significant figures.