This** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**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...

View
Full Document

- Spring '14
- FlorianEnescu
- Algebra, Dot Product, Vector Motors, dihedral angle, cos cos ↵hcos, 70.5 deg