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The magnitude of a sum of forces is equal to the sum of the individual force magnitudes,
each weighted by the cosine of the individual force relative to the direction of the total force.
Proof:
If a perpendicular is drawn from the starting and ending points of each force to the sum vector,
each segment has the length of the individual force multiplied by the cosine of the angle between the two directions.
Ludwig Resch
Note:
Formally, this is a projection of the force vector with the rank-1 matrix v•vT/v² of the direction vector v.
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