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Direction Cosine with Y-axis

Direction Cosine with Y-axis
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2017-11-22 09:20
AngleVectorGeometric Construction
This example demonstrates the calculation and visualization of the angle between a vector and the positive y-axis, along with its direction cosine. Key math concepts include vectors, direction cosines, and angle measurement. It uses GeoGebra commands like Vector, Point, and Angle to construct the illustration, making it suitable for high school students and university beginners in linear algebra or vector geometry.

GeoGebra Commands & Parameters

  1. Vector(O, P) → u
  2. Point(xAxis) → A
  3. Point(yAxis) → B
  4. Point(zAxis) → C
  5. Angle(A, O, P) → α
  6. Angle(B, O, P) → β
  7. Angle(C, O, P) → γ

AI Drawing Prompt Reference

Visualize the angle between a vector and the positive Y-axis along with its direction cosine, including an origin, vector, and points on the X, Y, and Z axes. Show the angles between the vector and each axis, then illustrate the calculation of the angle with the positive Y-axis and the direction cosine, suitable for beginners in vector geometry.
The prompt above was compiled from the original drawing commands and is for reference only.