Question

My question is with respect to PS 1-2b. There appears to some inconsistency between the diagram and the stated solution. It seems that the answer should be the (dir(u)+dir(v))/|dir(u)+dir(v)|, where dir(x) means unit vector in the direction of x.

Answer 1

Can you make a screen shot of the question/answer and post it?

Answer 2

It looks like they were sloppy writing up the answer.
First, to find the vector that bisects u and v normalize both to the same length (unit length is fine)
thus begin with
\[ \hat {u} = \frac{\vec{u}}{|u|} \]
and similarly for \(\hat v\)
as noted in the answer, \( \hat u + \hat v\) bisects the angle between the two vectors.
They want the unit length vector.
to make this vector unit length , divide by its magnitude, we get
\[ \frac{\hat u + \hat v}{| \hat u + \hat v| } \]
this is what I assume you mean by
(dir(u)+dir(v))/|dir(u)+dir(v)|

notice that the answer starts by stating u and v are unit length
and they then give the answer
\[ \frac{u + v}{| u+ v|} \]
which is the correct answer (if u and v are unit length)

the problem is that u and v in the question are not unit length
thus, in the answer, they should have started with \(\hat u \) and \(\hat v\)
(i.e. u and v normalized to unit length).

I would say they were a wee bit sloppy, but their answer is essentially correct. (they should put "hats" over u and v)

Answer 3

Thanks again phi.