# Worksheet: The Vector Product of Two Vectors

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

**Q1: **

Consider the two vectors and . Calculate .

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**Q2: **

Two vectors, and , have the same length and are perpendicular to each other. The vector product of and has a magnitude of 9. What is the length of each vector?

**Q3: **

The diagram shows two vectors, and , in three-dimensional space. Both vectors lie in the -plane. Each of the squares on the grid has a side length of 1. Calculate .

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**Q4: **

The diagram shows two vectors, and , in three-dimensional space. Both vectors lie in the -plane. Each of the squares on the grid has a side length of 1. Calculate .

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**Q5: **

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

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**Q6: **

Work out .

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**Q7: **

The diagram shows a rod that can rotate around point P. A force is applied to the end of the rod. Each of the squares of the grid has a side length equal to 1 m and 1 N. The torque on the rod is equal to the vector product of and . Calculate the magnitude of the torque on the rod.

**Q8: **

The diagram shows two vectors, and , in three-dimensional space. Both vectors lie in the -plane. Each of the squares of the grid has a side length of 1. Calculate .

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**Q9: **

The diagram shows a rod with a length of 1.5 m that can rotate around point P. A force with a magnitude of 12 N is applied to the end of the rod. What is the magnitude of the torque applied to the rod?

**Q10: **

Consider the two vectors and . Does point in the positive -direction or the negative -direction?

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**Q11: **

The diagram shows two vectors, and . Calculate the magnitude of the vector product of and . Give your answer to 2 significant figures.

**Q12: **

Consider the two vectors and .

Calculate .

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Calculate .

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**Q13: **

Complete the following: The diagram shows six vectors, , , , , , and , in three-dimensional space. All of the vectors lie in the -plane, and all have the same length. The vector product of and has the greatest magnitude.

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**Q14: **

The diagram shows two vectors, and , in three-dimensional space. Both vectors lie in the -plane. Each of the squares of the grid has a side length of 1. Calculate .

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**Q15: **

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

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**Q16: **

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

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**Q17: **

The diagram shows a rod with a length of 2.2 m that can rotate around point P. A force with a magnitude of 35 N is applied to the end of the rod. What is the magnitude of the torque applied to the rod? Give your answer to 2 significant figures.

**Q18: **

Work out .

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**Q19: **

The diagram shows two vectors, and . The magnitude of the vector product of and is 6.8. Calculate the angle between the two vectors, . Give your answer to 2 significant figures.

**Q20: **

Consider the two vectors and . has a length of 4 and has a length of 13. The angle between them is . Calculate the magnitude of . Give your answer to 3 significant figures.

- A50.9
- B8.80
- C245
- D10.8
- E16.6

**Q21: **

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**Q22: **

Consider the two vectors and . Calculate .

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**Q23: **

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