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In this lesson, we will learn how to calculate the vector product of two vectors and how to use the vector product to find the angle between two vectors.

Q1:

Calculate the product .

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 .

Q3:

Consider the vectors .

Find .

Find the angle between and .

Q4:

A convoy of vehicles has a velocity vector .

What is the unit vector of the convoyβs direction of motion?

At what angle north of east does the convoy move?

Q5:

The positive π₯ -axis is horizontal to the right for the vectors shown.

What is the vector product β π΄ Γ β πΆ ?

What is the vector product β π΄ Γ β πΉ ?

What is the vector product β π· Γ β πΆ ?

What is the vector product β π΄ Γ ( β πΉ + 2 β πΆ ) ?

What is the vector product β π Γ β π΅ ?

What is the vector product β π Γ β π΅ ?

What is the vector product ( 3 β π β β π ) Γ β π΅ ?

Q6:

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 ?

Q8:

Q9:

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?

Q12:

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

Q13:

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

Q14:

Find the angle between the two vectors β π¦ = ( 2 β π + 4 β π + 8 β π ) and β π§ = ( 6 β π + 4 β π + 2 β π ) in degrees. Which of the following best matches the result?

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