Vector maximisationish question (1 Viewer)

[Average Boreduser]

So I tried doing this using vectors and completely fked it somehow. My method was to find the dot prod. and then maximise using the fact that the magnitudes of the vectors can be expressed as a constant k. Implicitly diffed and made dtheta/dy the subject. but didn't work out in the end... I have provided my method below. can someone show me if I was on the right track at least or?

 

[Average Boreduser]

Just realised why it doesnt work (since I cant prove the concavity and since y is changing and therefore it cant be considered constant). is there any way to do this using vectors per chance?

 

[Average Boreduser]

And why tf do u need moles theory to understand the qn before it lmfao... Literally cheat code for chemistry students.

 

[Trebla]

If you want to do it with vectors, find the dot product of their unit vectors which equals the cosine of the angle you want to maximise.

Since cosine is decreasing in the plausible values of the angle, maximising the angle is equivalent to minimising the cosine of that angle, which your dot product has retrieved as a function of y.