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 A in component form.

  • A6+3ij
  • B3+6ij
  • C63ij
  • D36ij
  • E63ij

Q2:

The vector A can be written in the form 𝑎+𝑎ij.

What is the value of 𝑎?

What is the value of 𝑎?

Q3:

Write A in component form.

  • A32ij
  • B2+3ij
  • C32ij
  • D23ij
  • E3+2ij

Q4:

The diagram shows a vector, A, that has a vertical component with a magnitude of 130. The angle between the vector and the 𝑥-axis is 64. What is the magnitude of the vector? Give your answer to 2 significant figures.

Q5:

The diagram shows a vector, A, that has a horizontal component with a magnitude of 39. The angle between the vector and the 𝑥-axis is 18. What is the magnitude of the vector? Give your answer to 2 significant figures.

Q6:

The diagram shows a vector A that has a magnitude of 22. The angle between the vector and the 𝑥-axis is 36. Work out the horizontal component of the vector. Give your answer to 2 significant figures.

Q7:

The vector A can be written in the form 𝑎+𝑎ij.

What is the value of 𝑎?

What is the value of 𝑎?

Q8:

The vector A can be written in the form 𝑎+𝑎ij.

What is the value of 𝑎?

What is the value of 𝑎?

Q9:

Write A in component form.

  • A48ij
  • B48ij
  • C4+8ij
  • D84ij
  • E8+4ij

Q10:

The diagram shows a vector, A, that has a magnitude of 43. The angle between the vector and the 𝑥-axis is 66. Work out the vertical component of the vector. Give your answer to 2 significant figures.

Q11:

The diagram shows a vector, A, which has a magnitude of 430. The angle between the vector and the 𝑥-axis is 85.0. Work out the vertical component of the vector. Give your answer to 3 significant figures.

Q12:

The diagram shows a vector, A, that has a magnitude of 55. The angle between the vector and the 𝑥-axis is 82. Work out the horizontal component of the vector. Give your answer to the nearest whole number.

Q13:

The diagram shows a vector, A, that has a magnitude of 29. The angle between the vector and the 𝑥-axis is 60. Give this vector in component form. Round all of the numbers in your answer to the nearest whole number.

  • A15+25ij
  • B15+25ij
  • C25+15ij
  • D1525ij
  • E2515ij

Q14:

The diagram shows a vector, A, that has a magnitude of 84. The angle between the vector and the 𝑥-axis is 39. Work out the horizontal component of the vector. Give your answer to the nearest whole number.

Q15:

The diagram shows a vector, A, that has a magnitude of 24. The angle between the vector and the 𝑥-axis is 43. Give this vector in component form. Round all numbers in your answer to the nearest whole number.

  • A1816ij
  • B16+18ij
  • C18+16ij
  • D18+16ij
  • E16+18ij

Q16:

The diagram shows a vector, A, that has a magnitude of 91. The angle between the vector and the 𝑥-axis is 26. Give this vector in component form. Round all of the numbers in your answer to the nearest whole number.

  • A4082ij
  • B40+82ij
  • C82+40ij
  • D8240ij
  • E82+40ij

Q17:

The diagram shows a vector, A, that has a magnitude of 75. The angle between the vector and the 𝑥-axis is 40. Work out the vertical component of the vector. Give your answer to the nearest whole number.

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