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
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°)
Use Known Lengths:
If a specific length or additional vector relationships are provided, one could use them to derive the length of vector b.
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
Formula Application:
Given an equation involving |b|, substitute known values to isolate and solve for |b|.