# Worksheet: Finding the Components of a Vector

In this worksheet, we will practice finding the x and y components of a vector given its magnitude and the angle between the vector and one of the axes.

**Q1: **

Write in component form.

- A
- B
- C
- D
- E

**Q2: **

The vector can be written in the form .

What is the value of ?

What is the value of ?

**Q3: **

Write in component form.

- A
- B
- C
- D
- E

**Q4: **

The diagram shows a vector, , that has a vertical component with a magnitude of 130. The angle between the vector and the is . What is the magnitude of the vector? Give your answer to 2 significant figures.

**Q5: **

The diagram shows a vector, , that has a horizontal component with a magnitude of 39. The angle between the vector and the is . What is the magnitude of the vector? Give your answer to 2 significant figures.

**Q6: **

The diagram shows a vector that has a magnitude of 22. The angle between the vector and the is . Work out the horizontal component of the vector. Give your answer to 2 significant figures.

**Q7: **

The vector can be written in the form .

What is the value of ?

What is the value of ?

**Q8: **

The vector can be written in the form .

What is the value of ?

What is the value of ?

**Q9: **

Write in component form.

- A
- B
- C
- D
- E

**Q10: **

The diagram shows a vector, , that has a magnitude of 43. The angle between the vector and the is . Work out the vertical component of the vector. Give your answer to 2 significant figures.

**Q11: **

The diagram shows a vector, , which has a magnitude of 430. The angle between the vector and the -axis is . Work out the vertical component of the vector. Give your answer to 3 significant figures.

**Q12: **

The diagram shows a vector, , that has a magnitude of 55. The angle between the vector and the is . Work out the horizontal component of the vector. Give your answer to the nearest whole number.

**Q13: **

The diagram shows a vector, , that has a magnitude of 29. The angle between the vector and the is . Give this vector in component form. Round all of the numbers in your answer to the nearest whole number.

- A
- B
- C
- D
- E

**Q14: **

The diagram shows a vector, , that has a magnitude of 84. The angle between the vector and the is . Work out the horizontal component of the vector. Give your answer to the nearest whole number.

**Q15: **

The diagram shows a vector, , that has a magnitude of 24. The angle between the vector and the is . Give this vector in component form. Round all numbers in your answer to the nearest whole number.

- A
- B
- C
- D
- E

**Q16: **

The diagram shows a vector, , that has a magnitude of 91. The angle between the vector and the is . Give this vector in component form. Round all of the numbers in your answer to the nearest whole number.

- A
- B
- C
- D
- E

**Q17: **

The diagram shows a vector, , that has a magnitude of 75. The angle between the vector and the is . Work out the vertical component of the vector. Give your answer to the nearest whole number.