How do you write a unit vector from 8i-4j-8k?

[franky2727]

i get that a unit vector is U/modU but how would it be written for example 8i-4j-8k would it be simply (8i-4j-8k)/144?

 

[CompuChip]

Notation for the normalized vector $\vec u$ is also $\hat u$. Note, that it is $\vec u / ||\vec u||$ and not $\vec u / || \vec u ||^2$.

 

[franky2727]

ah sorry i ment over root 144 . apart from that is the way i wrote it fine or would i have to split it into I J and K parts?

 

[CompuChip]

It doesn't matter;

(8i-4j-8k)/12 = (8/12) i - (4/12) j - (8/12) k.

 

[HallsofIvy]

It doesn't matter;

(8i-4j-8k)/12 = (8/12) i - (4/12) j - (8/12) k.

Or even better (2/3)i- (1/3)j- (2/3)k

 

[CompuChip]

Or even better (2/3)i- (1/3)j- (2/3)k

Which is then again equivalent to
(2i - j - 2k) / 3
or
2(i - 1/2 j - k) / 3

Take your pick (or make your own :D)