# Vector Quantities: Can Unit of Measurement Reveal Vector?

• Char. Limit
In summary, the conversation discusses whether the units of a physical measurement determine if the quantity is a vector or scalar. The conclusion is that the units do not determine this, as both vector and scalar quantities can have the same units. The concept of a vector having units is also discussed, with the idea that a vector itself does not have units but its components may have units. Overall, it is concluded that the concept of units is more relevant to scalar quantities.
Char. Limit
Gold Member
Can someone tell, using the unit of a physical measurement, if the measurement is a vector? For example, without knowing about force, can one tell by the unit kg-m/s^2 that force is a vector?

I'm trying to say, for example, thay since the m in kg-m/s^2 is a vector (for example), the whole thing is a vector... I probably sound dumb...

Does the unit or system have a magnitude of some sort? Does it have a direction of some sort? If it meets both conditions, it's a vector.

Well... let's say I invented a new, unused unit... I'll say m^2/s. Could you tell, just by that unit, if the quantity is a vector?

Char. Limit said:
Well... let's say I invented a new, unused unit... I'll say m^2/s. Could you tell, just by that unit, if the quantity is a vector?
No. The units have nothing to do with whether the quantity is a vector or scalar. I could perhaps invent a vector quantity with the units m^2/s and a scalar quantity with the same units. Or even several of each.

Example: take the unit of length, the meter. There is a vector quantity, displacement, and a scalar quantity, distance, that are both measured in meters.

Example 2: Current, measured in amperes, can be a scalar or vector depending on who you ask.

Caveat: for some units, there don't happen to be any meaningful vector quantities associated with them. For example, off the top of my head I can't think of a vector quantity with units of mass. Or time. But there's no mathematical reason that one couldn't be created.

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Thanks.

I am confusing myself a little. When you say "the velocity is 5 m/s north", you really are saying "the magnitude of the velocity vector is 5 m/s, and the direction is north"- so the actual unit is attributed to the magnitude, a scalar. The vector itself doesn't have a unit, but is composed of a set of scalar components, each with their units. From this perspective, only scalars can have units. I could feasibly construct a vector [x,y] in which x and y are scalars with different units, for example in polar coordinates x is a distance and y is dimensionless (the polar angle, in radians, so a ratio of two distances), then there is no convention I know of how to give this vector a unit.

For me it is meaningless to say the vector has units... the vector gives you the location of a point in whatever space you are talking about, and a point does not have units. The distance in that space to a set of normal planes can have units, however, so each component can have units.
Any disagreement with this view?

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## 1. What is a vector quantity?

A vector quantity is a physical quantity that has both magnitude and direction. It is represented by an arrow, where the length of the arrow represents the magnitude and the direction of the arrow represents the direction of the quantity.

## 2. How are vector quantities different from scalar quantities?

Scalar quantities only have magnitude, while vector quantities have both magnitude and direction. For example, speed is a scalar quantity as it only tells us the magnitude of an object's motion, while velocity is a vector quantity as it tells us both the magnitude and direction of an object's motion.

## 3. How is the unit of measurement related to vector quantities?

The unit of measurement for a vector quantity must include both magnitude and direction. For example, the unit for velocity is meters per second (m/s) which includes both the magnitude (meters) and the direction (per second).

## 4. How does the unit of measurement reveal the direction of a vector quantity?

The unit of measurement can reveal the direction of a vector quantity by indicating which direction it is pointing. For example, if the unit of measurement for a velocity vector is meters per second east (m/s east), it tells us that the object is moving eastward.

## 5. Can the unit of measurement change the magnitude of a vector quantity?

No, the unit of measurement does not affect the magnitude of a vector quantity. The magnitude of a vector quantity is determined by the length of the arrow representing it, which does not change with the unit of measurement.

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