Engineering Calculus Notes 60

Engineering Calculus Notes 60 - 48 CHAPTER 1 COORDINATES...

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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 bardbl , the projection of −→ g in the direction of the ramp. To abstract this situation, recall that a direction is specified by a unit vector. The (vector) projection of an arbitrary vector −→ v in the direction specified 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 −→ v = ( | −→
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