48 CHAPTER 1. COORDINATES AND VECTORS −→ g θ Figure 1.27: A weight on a ramp parallel to the ramp. Then −→ g ⊥ is cancelled by the structural forces in the ramp, and the net unopposed force is −→ g b , the projection of −→ g in the direction of the ramp. To abstract this situation, recall that a direction is speci±ed by a unit vector. The (vector) projection of an arbitrary vector −→ v in the direction speci±ed by the unit vector −→ u is the vector proj −→ u −→ v := ( | −→ v | cos θ ) −→ u where θ is the angle between −→ u and −→ v (Figure 1.28 ). Note that replacing −→ u proj −→ u −→ v F −→ v θ Figure 1.28: Projection of a Vector −→ u with its negative replaces θ with π − θ , and the projection is unchanged: proj − −→ u −→
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.