Perpendicular Vector

[tram]

lol, spech stands for specialist maths matty. What does spesh stand for???

And yea.....i though as much......TBH i reackon if you get the right examiner, you'd get away with it, but some examiners would be like.....NO, THAT'S WRONG, beta not to take the chance

[Mao]

Find the unit vector which bisects the angel between a = 2i - j +  2k and b = 4i +3k. Hint: First find the unit vectors in the directions of the given vectors) >:S

Here's how I can think of doing it... there's probably a much easier way though 
let u=a's unit vector and v=b's unit vector and z= required vector
so and

let the angle between u and v = 2x
therefore, the angle between u and z = x
and the angle between v and z = x


              
Say that
Solving and and and given that
We have 4 variables with 4 equations so it can be solved... (i used a calculator)
Two results were obtained because x has both an acute and obtuse solution, we only want the acute one
The exact solutions were hideous, so to two decimal places,
the other solution i think was the colinear obtuse solution,
as i said, i'm sure there must be an easier way, but this was the best that I could come up with!

My only other thoughts would be to average the i, j and k components of vectors a and b and find a unit vector of the result.
Now that I think about it, that way should work and is much easier than my previous solution which I think is probably wrong, but it took ages to type so I'm leaving it there!

If you draw it out, you'll see that bisects the angle between a and b. Thus, the unit vector of the angle bisector is

[AzureBlue]

lol, spech stands for specialist maths matty. What does spesh stand for???

Ok then... spech = specialist maths and  spesh = spestroscopy

[tram]

^YESSSSS TOTALLY AGREED

[Mao]

Stop this pointless crap on spesh vs spech¹, or else.


¹That is unless you find something even more inconsequential to get hyped up about, like 'does my arse look big in this?'. Yes it fucking does, you sound like a fucking child.

[tram]

point taken. I'll stop