Fundamental vector projection question

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SUMMARY

The discussion focuses on projecting a vector defined by (v1, v2, v3) onto a plane characterized by a point (p1, p2, p3) and a normal vector (n1, n2, n3). The correct method involves first calculating the projection of the vector onto the normal vector using the standard projection formula. Subsequently, subtracting this projection from the original vector yields the component orthogonal to the normal, effectively providing the projection onto the plane.

PREREQUISITES
  • Understanding of vector projection concepts
  • Familiarity with normal vectors in three-dimensional space
  • Knowledge of the cross-product operation
  • Proficiency in applying mathematical formulas for vector operations
NEXT STEPS
  • Study the standard projection formula for vectors
  • Learn how to calculate the projection of a vector onto a normal vector
  • Explore the geometric interpretation of vector projections
  • Practice problems involving vector projections onto planes
USEFUL FOR

Students in mathematics or physics, educators teaching vector calculus, and anyone involved in computational geometry or 3D modeling.

jrm2002
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Homework Statement



1.I have a vector defined by (v1,v2,v3).
2. I want to project this vector on a plane such that a point on that plane is defined by (p1,p2,p3).Also, the normal to the plane is given by (n1,n2,n3)
3.Can anyone help me to the projection of the vector on this plane?

Please help


Homework Equations





The Attempt at a Solution



Tried using cross-product--but solution not validating.
 
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The first thing you can do is take the projection of the vector (v1,v2,v3) on the normal vector (n1,n2,n3). Use the standard projection formula for that. Subtracting projection from (v1, v2, v3) will give you the component of (v1, v2, v3) orthogonal to (n1, n2, n3). In other words, the projection onto the plane.
 

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