Vector Resultant and Pythagorean Theorem
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Questions and Answers

What is the resultant of two or more vectors?

  • The single vector that has the same effect as the individual vectors (correct)
  • A vector that is perpendicular to the individual vectors
  • The vector that is opposite in direction to the individual vectors
  • The vector that has the greatest magnitude among the individual vectors

    • What is the Pythagorean Theorem used for?

  • To resolve vectors into their components
  • To add vectors at any angle
  • To find the direction of the resultant vector
  • To find the magnitude of the resultant vector when two vectors are added at right angles (correct)

    • What is the primary advantage of the component method?

  • It provides a quick and easy way to add vectors
  • It is only used to find the magnitude of the resultant vector
  • It can be used to add vectors at any angle (correct)
  • It can only be used to add vectors at right angles

    • What is the first step in adding vectors using the component method?

    <p>Resolve each vector into its x- and y-components</p> Signup and view all the answers

    What is the term for the magnitude of the resultant vector when two vectors are added at right angles?

    <p>Hypotenuse</p> Signup and view all the answers

    What is the resultant vector also known as?

    <p>Net vector or sum vector</p> Signup and view all the answers

    Study Notes

    Vector Resultant

    • The resultant of two or more vectors is the single vector that has the same effect as the individual vectors.
    • It is the vector sum of the individual vectors.
    • The resultant vector is also known as the net vector or the sum vector.

    Pythagorean Theorem

    • The Pythagorean Theorem is used to find the magnitude of the resultant vector when two vectors are added at right angles.
    • The theorem states: a² + b² = c², where a and b are the magnitudes of the two vectors, and c is the magnitude of the resultant vector.
    • The angle between the two vectors is 90 degrees.

    Component Method

    • The component method is a way to add vectors by breaking them down into their horizontal and vertical components.
    • The horizontal component is the x-component, and the vertical component is the y-component.
    • To add vectors using the component method:
      1. Resolve each vector into its x- and y-components.
      2. Add the x-components and y-components separately.
      3. Use the resulting x- and y-components to find the magnitude and direction of the resultant vector.
    • The component method can be used to add vectors at any angle, not just at right angles.

    Vector Resultant

    • The resultant of two or more vectors is the single vector that has the same effect as the individual vectors.
    • It is the vector sum of the individual vectors.
    • The resultant vector is also known as the net vector or the sum vector.

    Pythagorean Theorem

    • Used to find the magnitude of the resultant vector when two vectors are added at right angles.
    • The theorem states: a² + b² = c², where a and b are the magnitudes of the two vectors, and c is the magnitude of the resultant vector.
    • The angle between the two vectors is 90 degrees.

    Component Method

    • A way to add vectors by breaking them down into their horizontal and vertical components.
    • The horizontal component is the x-component, and the vertical component is the y-component.
    • The component method involves:
      • Resolving each vector into its x- and y-components.
      • Adding the x-components and y-components separately.
      • Using the resulting x- and y-components to find the magnitude and direction of the resultant vector.
    • The component method can be used to add vectors at any angle, not just at right angles.

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    Description

    Understand the concept of vector resultant and its application in calculating the magnitude using Pythagorean Theorem. Learn how to find the net vector and its magnitude.

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