Why use unit vector for this, and not for that?

This requires taking into account all three directions involved, so vectors are necessary. The car problem only had one direction, so the unit vector was not needed for calculations. However, the second problem did not use the unit vector and may have resulted in an opposite outcome. In summary, the first problem used the unit vector to calculate a moment about an axis, while the second problem required vectors to account for all three directions and did not use the unit vector.
  • #1
viet_jon
131
0
the car problem in my text uses the unit vector, and the second one doesn't...

how come?


zxcv.jpg


zxc-1.jpg
 
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  • #2
The second problem is more complex and requires vectors to take care of the 3 directions involved. The first (car) problem has only one direction so no need for vectors.
 
  • #3
but it did the opposite of just that.

the car used 'unit' vector...

while the second does not use the 'unit' vector
 
  • #4
The first problem is asking for a moment about an axis. I'm pretty sure this is why you have to employ the unit vector in your calculations. If i recall correctly (been awhile since I was in statics) the unit vector here will be j or [0i 1j 0k]. Is that familiar?

The second problem is asking for a moment about a point.
 

FAQ: Why use unit vector for this, and not for that?

Why is a unit vector preferred over a regular vector?

Unit vectors have a magnitude of 1 and are used to represent the direction of a vector without affecting its scale. This makes them useful for calculations and simplifies the representation of complex vector quantities.

Can a unit vector be used for any type of vector?

Yes, a unit vector can be used for any type of vector, regardless of its magnitude or direction. It is a standardized way of representing a vector's direction and can be applied to any vector quantity.

How does using unit vectors affect vector operations?

Using unit vectors in vector operations simplifies calculations as it eliminates the need for scaling and allows for easier manipulation and comparison of vector quantities.

Are unit vectors only used in 2-dimensional vectors?

No, unit vectors can be applied to vectors in any number of dimensions. They are commonly used in 3-dimensional vectors, but can also be used in higher dimensions.

Are there any drawbacks to using unit vectors?

The main drawback of using unit vectors is that they do not retain information about the magnitude of a vector. This means that any calculations involving vector magnitude must be done separately.

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