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
=2x)
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!
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