- #1

Perion

c = |b|a + |a|b

then vector c bisects the angle theta between vectors a and b. [0 < theta <= Pi]

I used the vectors' component forms and let a = <a1,a2> and b = <b1,b2> and then worked out the equations for the cosine of the angles between (1) a and c, and (2) c and b. I then tried to determine if (1) and (2) were equal. I used the equations

(1) cos(phi1) = (a.c)/|a||c| and

(2) cos(phi2) = (c.b)/|c||b| [a.c and c.b are dot products]

Unfortunately I came up with some rather long, complicated, component expressions which proved quite cumbersome to test for equality. I suspect that James Stewart (my textbook author) had an easier method in mind (maybe using projections) that didn't involve such algebraic gymnastics. Am I missing some obviously simple method to go about this?

Thanks,

Perion