Really not sure how you would show this Bisection??

[ku1005]

Let a and b be non zero vectors in R^3. Show that the vector |a|b+|b|a bisects the angle bewteen a and b.

it says as a hint you need to recall cos2(theta)= 2cos^2(theta)-1

but im really lost as to how this helps??

any suggestions would be great!!!

cheers

just another point...in my head and graphically this makes sense, its just a matter of showing this algebraicly ??

 

[pka]

The angle between two vectors is \(\displaystyle acr\cos \left( {\frac{{a \cdot b}}{{\left\| a \right\|\left\| b \right\|}}} \right)\).

Show that the two subangles are congruent.
\(\displaystyle \L acr\cos \left( {\frac{{a \cdot \left( {\left\| a \right\|b + \left\| b \right\|a} \right)}}{{\left\| a \right\|\left\| {\left\| a \right\|b + \left\| b \right\|a} \right\|}}} \right) = \limits^? acr\cos \left( {\frac{{b \cdot \left( {\left\| a \right\|b + \left\| b \right\|a} \right)}}{{\left\| b \right\|\left\| {\left\| a \right\|b + \left\| b \right\|a} \right\|}}} \right)\)