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Unformatted text preview: bisects the angle between u and v . We make this a unit vector: u + v .  u + v  See fgure. 3. a) See the sketch with part (b). It is clear that no matter what the angle ↵ the vector w 1 has a rightward component. b) In the sketch we’ve labeled the projection we want as w 2 . We see easily that  w 1  = a cos ↵ and  w 2  = cos β  w 1  = a cos β cos ↵ . y Thus w 2 = a cos β cos ↵ h cos( ↵ + β ) , sin( ↵ + β ) i . l B l s The component oF w 2 in the i direction is a cos( ↵ ) cos( β ) cos( ↵ + β ). Since ↵ and β are between and ⇡ / 2 this component is negative exactly when w 2 ↵ + β > ⇡ / 2. (This is easily seen in the sketch as well.) w * 4 ↵ β > L w 1 S a 2...
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 Fall '14
 FlorianEnescu
 Algebra, Dot Product, Vector Motors, dihedral angle, cos cos ↵hcos, 70.5 deg

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