Why do we need projection of vectors

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    Projection Vectors
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Discussion Overview

The discussion centers on the concept of vector projection, specifically the projection of vector B onto vector A, and its applications in physics, particularly in resolving forces and calculating work. Participants explore the significance of this mathematical operation in various contexts.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant states that the projection of vector B on A is given by ||B||cos(theta), where theta is the angle between the two vectors, and questions the necessity of this calculation.
  • Another participant suggests that the projection is useful for determining the parallel contribution of vector B to the total, particularly in applications like resolving forces and calculating work.
  • A later reply reiterates the usefulness of projections in calculating work, emphasizing the relationship between force and distance in the direction of motion.
  • One participant references an external source that discusses the generalization of work calculations involving a constant force not aligned with the direction of movement, mentioning the dot product and its relation to the angle between vectors.

Areas of Agreement / Disagreement

Participants generally agree on the utility of vector projection in applications related to forces and work, but the discussion does not resolve the initial question of why the projection is necessary beyond these applications.

Contextual Notes

The discussion does not delve into specific assumptions or limitations regarding the definitions of vector projection or the contexts in which it is applied.

parshyaa
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I know that projection of vector B on A is ||B||cos(theta) where theta is the angle between vector A and B . But why do we find it . Is there any application for this
 
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it is useful in many applications when you want to know the parallel contribution of B to the total, eg in resolving a force or calculating work ie;

work = Force X distance in direction of motion
 
Ohkkk , thanks
houlahound said:
it is useful in many applications when you want to know the parallel contribution of B to the total, eg in resolving a force or calculating work ie;

work = Force X distance in direction of motion
k
 
read here from

https://en.wikipedia.org/wiki/Work_(physics);

"This calculation can be generalized for a constant force that is not directed along the line, followed by the particle. In this case the dot product F ⋅ ds = F cos θ ds, where θ is the angle between the force vector and the direction of movement.
 
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