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Direction Cosine with Z-axis

Direction Cosine with Z-axis
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2017-11-22 09:27
VectorTrigonometryCoordinate Geometry
This example demonstrates the calculation and visualization of the direction cosine between a vector and the Z-axis. It involves core math concepts like vectors, direction cosines, and angle measurement. Constructed using GeoGebra commands such as Vector, Point, and Angle, it is suitable for high school coordinate geometry and solid geometry education, aiding in understanding the relationship between spatial vectors and coordinate axes.

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

Draw a vector u from the origin O to point P. Then place points A, B, and C on the x-axis, y-axis, and z-axis respectively. Measure the angles α, β, and γ between vector u and the x-axis, y-axis, and z-axis to visualize the direction cosines.
The prompt above was compiled from the original drawing commands and is for reference only.