# 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. 