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Direction Cosines

Direction Cosines
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2017-11-22 09:38
AngleVectorGeometric Construction
This example demonstrates the direction cosines of a point P in space and their relationship with the vector OP. It involves core concepts like vectors, points, angles, and the direction cosine theorem. Constructed using Vector, Point, and Angle commands to form points O, P, vector u, and angles α, β, γ. Suitable for high school and above students studying vectors and spatial geometry to understand the calculation and geometric meaning of direction cosines.

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 point O and point P in 3D space, and draw the vector OP from O to P. Then, mark points A, B, and C on the x-axis, y-axis, and z-axis passing through O respectively. Next, calculate and plot angles α, β, and γ, which are the angles between vector OP and the x-axis, y-axis, and z-axis respectively. Finally, combine these points and angles to show the direction cosines of vector OP and their relationship with the coordinate axes.
The prompt above was compiled from the original drawing commands and is for reference only.