Recording-2025-02-06T23:39:42.699Z

Problem Statement

  • A vector is referenced with an angle of 30 degrees.

  • The objective is to determine the length of vector b based on this angle.

Understanding Vectors

  • Vector Definition: A vector is a quantity that has both magnitude (length) and direction.

  • Angle Relevance: The angle associated with a vector helps define its direction in a coordinate plane.

Information Breakdown

  • Given:

    • Angle (θ) = 30 degrees.

  • Required:

    • Length of vector b (|b|).

Steps to Solve

  1. Identify Components:

    • If the vector b is positioned at an angle of 30 degrees from a coordinate axis (typically the x-axis), you can express it in terms of its components using trigonometry:

      • x-component = |b| * cos(30°)

      • y-component = |b| * sin(30°)

  2. Use Known Lengths:

    • If a specific length or additional vector relationships are provided, one could use them to derive the length of vector b.

  3. Example Calculation:

    • Assuming an arbitrary total length or resulting values from other vector components is known, plug in the angle:

      • cos(30°) = √3/2 ≈ 0.866

      • sin(30°) = 1/2 = 0.5

  4. Formula Application:

    • Given an equation involving |b|, substitute known values to isolate and solve for |b|.

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