# Worksheet: The Scalar Product of Two Vectors

In this worksheet, we will practice calculating the scalar product of two vectors using both the components of the vectors and the magnitudes of the two vectors and the angle between them.

**Q1: **

The diagram shows two vectors, and . Each of the grid squares in the diagram has a side length of 1. Calculate .

**Q2: **

The diagram shows two vectors, and . Each of the grid squares in the diagram has a side length of 1. Calculate .

**Q3: **

An object moves along a straight line. As the object moves, it is acted upon by a constant force. The diagram shows the displacement of the object, , and the force acting on it, . Each of the grid squares in the diagram has a side length of 1. How much work is done by the force?

**Q4: **

The diagram shows two vectors, and . Each of the grid squares in the diagram has a side length of 1. Calculate .

**Q5: **

The diagram shows two vectors, and . What is the scalar product of and ?

**Q6: **

An object moves along a straight line. As the object moves, it is acted upon by a constant force. The diagram shows the displacement of the object, , and the force acting on it, . Each of the grid squares in the diagram has a side length of 1 in both meters and newtons. Calculate .

**Q7: **

**Q8: **

The diagram shows two vectors, and . What is their scalar product?

**Q9: **

An object moves along a straight line between times and , moving a distance of 3 m. A constant force with a magnitude of 8 N acts on the object as it moves. The force acts at an angle of to the direction of motion of the object. What is the scalar product of the force acting on the object and its displacement over the given time interval? Give your answer to 2 significant figures.

**Q10: **

The diagram shows two vectors, and . What is their scalar product?

**Q11: **

**Q12: **

The diagram shows two vectors, and . What is the scalar product of and ? Give your answer to 2 significant figures.

**Q13: **

Consider the two vectors and . Calculate .

**Q14: **

**Q15: **

Fill in the blank: The diagram shows several vectors on a grid. Each of the grid squares in the diagram has a side length of 1. The scalar product of and is equal to zero.

- A
- B
- C
- D
- E

**Q16: **

**Q17: **

Consider the two vectors , with a magnitude of 7.7, and , with a magnitude of 15. The scalar product of the two vectors is 27. What is the angle between the vectors? Give your answer to 3 significant figures.

**Q18: **

**Q19: **

The diagram shows two vectors, and . What is the scalar product of and ? Give your answer to 2 significant figures.

**Q20: **

A constant force of acts on an object, causing it to move. After an amount of time, the displacement of the object from its initial position is . Calculate .

**Q21: **

Consider the two vectors of magnitude 12 and of magnitude 26. The angle between them is . What is the scalar product of and ? Give your answer to 3 significant figures.

- A137
- B312
- C289
- D38.0
- E117