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 (B)</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 (A)</p> Signup and view all the answers

What is the resultant vector also known as?

<p>Net vector or sum vector (C)</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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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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