Writing Unit Vectors: A Quick Guide for Scientists

In summary, a unit vector is denoted by \hat u and is equal to \vec u / ||\vec u||. It is important to note that the denominator is ||\vec u|| and not || \vec u ||^2. The notation for a normalized vector can also be written as \vec u / ||\vec u||. When written in components, it can be simplified to (2/3)i- (1/3)j- (2/3)k or any equivalent form.
  • #1
franky2727
132
0
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?
 
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  • #2
Notation for the normalized vector [itex]\vec u[/itex] is also [itex]\hat u[/itex]. Note, that it is [itex]\vec u / ||\vec u||[/itex] and not [itex]\vec u / || \vec u ||^2[/itex].
 
  • #3
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?
 
  • #4
It doesn't matter;

(8i-4j-8k)/12 = (8/12) i - (4/12) j - (8/12) k.
 
  • #5
CompuChip said:
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 :tongue2:
 
  • #6
HallsofIvy said:
Or even better (2/3)i- (1/3)j- (2/3)k :tongue2:

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)
 

1. What is a unit vector?

A unit vector is a vector with a magnitude of 1. It represents the direction of a vector without considering its length or scale.

2. How do I write a unit vector?

To write a unit vector, you need to first find the magnitude of the vector. Then, divide each component of the vector by the magnitude to get the unit vector. The resulting vector will have a magnitude of 1.

3. What is the notation used for unit vectors?

The notation used for unit vectors is a caret or hat symbol (^) above the vector variable. For example, a unit vector of vector v would be written as âv.

4. Can a unit vector have negative components?

Yes, a unit vector can have negative components. The magnitude of the vector will still be 1, but the direction will be opposite of the positive direction.

5. How are unit vectors used in vector operations?

Unit vectors are used to represent the direction of a vector in vector operations. They can be multiplied by a scalar to change the magnitude of the vector, or added/subtracted to other vectors to find the resultant vector.

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