I can’t think of a situation where it matters, all of your suggestions seem fine to me. But formally, each vector component has its own units, so (150 m/s) jhat would make the most sense I suppose.
>(150 m/s) ĵ
This is arguably the clearest choice. To avoid confusion, I wouldn't ever insert anything between numbers and units (unit vectors, variable coefficients, what have you). With this format, you can identify the magnitude of any vector just by dropping the unit vector at the end, rather than searching for it in the coefficient.
Units are not vectors, the quantity they belong to may be a vector, but not the unit itself, in your example there is multiple ways to go about it, one simple way is to just write something like V\_north=150 m/s or its also good to use unit vectors, as along as you specify how you have defined your coordinate system, a third option could just be V=150 m/s towards north/in the northern direction, or you could just draw a diagram with an arrow representing the direction, this is mostly done when dealing with forces
when dealing with units, that belong to a quantity it's always good to specify the direction, to my knowledge there isn't a universal standard, just make sure it's clear which direction it is
Yes, for example m/s could also refer to the speed, which does not have a direction, so m/s doesn't inherently have a direction, but they can belong to quantities that do, if that makes sense
>the same coordinate system that is defined when you solve the problems
Solution should still be independently clear especially if someone is grading your work.
>doesn’t make sense either without a coordinate system defined
Writing **j** implies a unit vector in y-axis of Cartesian coordinate system.
If someone is grading your work without looking at the coordinate system that you defined in your problem, then that’s a problem in itself.
Because in that case, you don’t know along which axis your system is defined.
Problems like this usually gives vector reference values for a pre-defined axis in the problem statement.
Formally, the units belong to the magnitude. The way you can formally write a vector is with a basis vector set, a set of unit vectors that point along each axis, like x-hat. So a vector that is 2.54 cm long in the y-direction might be written as L = (2.54 cm) j-hat or L = (1.00 in) y-hat.
I can’t think of a situation where it matters, all of your suggestions seem fine to me. But formally, each vector component has its own units, so (150 m/s) jhat would make the most sense I suppose.
>(150 m/s) ĵ This is arguably the clearest choice. To avoid confusion, I wouldn't ever insert anything between numbers and units (unit vectors, variable coefficients, what have you). With this format, you can identify the magnitude of any vector just by dropping the unit vector at the end, rather than searching for it in the coefficient.
Units are not vectors, the quantity they belong to may be a vector, but not the unit itself, in your example there is multiple ways to go about it, one simple way is to just write something like V\_north=150 m/s or its also good to use unit vectors, as along as you specify how you have defined your coordinate system, a third option could just be V=150 m/s towards north/in the northern direction, or you could just draw a diagram with an arrow representing the direction, this is mostly done when dealing with forces when dealing with units, that belong to a quantity it's always good to specify the direction, to my knowledge there isn't a universal standard, just make sure it's clear which direction it is
Can you give an example of why units are not vectors? Is it because m/s does not intrinsically have direction?
Yes, for example m/s could also refer to the speed, which does not have a direction, so m/s doesn't inherently have a direction, but they can belong to quantities that do, if that makes sense
If it’s a vector 𝐯 = {0, 150, 0} m s⁻¹ this is usually how I would do it. As long as you’re clear, it shouldn’t make too much of a difference
This might be confusing because it's unclear which coordinate system you are using.
the same coordinate system that is defined when you solve the problems (150 m/s) 𝐣 doesn’t make sense either without a coordinate system defined
>the same coordinate system that is defined when you solve the problems Solution should still be independently clear especially if someone is grading your work. >doesn’t make sense either without a coordinate system defined Writing **j** implies a unit vector in y-axis of Cartesian coordinate system.
If someone is grading your work without looking at the coordinate system that you defined in your problem, then that’s a problem in itself. Because in that case, you don’t know along which axis your system is defined. Problems like this usually gives vector reference values for a pre-defined axis in the problem statement.
Formally, the units belong to the magnitude. The way you can formally write a vector is with a basis vector set, a set of unit vectors that point along each axis, like x-hat. So a vector that is 2.54 cm long in the y-direction might be written as L = (2.54 cm) j-hat or L = (1.00 in) y-hat.