Can someone explain the difference between a scalar and vector quantity?

Question

I need to know what the difference is between them to answer these questions:

Which of the following is NOT a vector quantity?
a.) 2 miles per hour
b.) 2 pounds
c.) 2 newtons
d.) 2 kilometers per hour east
e.) 2 dynes

Which of the following is NOT a scalar quantity?
a.) 2 miles per hour
b.) 2 kilograms
c.) 2 apples
d.) 2 ounces
e.) 2 liters

I'm not looking for you to answer the questions as I already know the answers[ a.) and d.) - from the book] but I need to know the difference between a scalar and vector quantity so I can answer them myself. The book is simply a workbook and has no explanations.

Answer 1

A scalar is just a number, and a vector is a number with a direction involved.

In the first question, pounds, newtons, and dynes are all *forces*. A force can't exist as just a number; force has to be directed somewhere. 2 kilometers/hour east gives you a number and a direction. The answer a) is just a speed. You can know something is traveling 2 miles/hr without knowing what direction it's traveling. You can't say something is simply exerting 2 pounds of force; it has to be exerting it on something else.

In the second question, we've already said that 2 miles per hour was a scalar. 2 apples is obviously directionless. 2 kilograms and 2 liters just tell you how much of something you have. 2 ounces here must mean ounces in a pound rather than fluid ounces. So these are a weight, which is again a force and has to be directed somewhere.

Answer 2

Those two questions are not worded very well. It's true that "force is a vector"; and it's also true that "pounds are a unit of force"; but it is not quite true that "2 pounds" is a vector. I understand the point that the question's author (your teacher?) is trying to make; but he/she makes it poorly.

Technically speaking, in Question #1, there is only one choice which IS a vector, and that is "d". And technically, in Question #2, ALL of the choices are scalars.

That is because, technically, a vector is a quantity that is expressed by using TWO numbers; one number to express a "magnitude" (an amount); and the other number to express a direction. (Or, if the vector is in 3 dimensions, then you use three numbers; one to express the magnitude, and two to express the direction).

"East" can be translated into a number (you could say it's "90 degrees" in some frame of reference); so "2 kilometers per hour east" counts as a vector. None of the other choices (in either question) is truly a vector, however; because the simple fact is, it's not a vector if it's described using only one number.

In physics, certain concepts (such as "force" and "momentum") are not very useful unless you attach a direction to them; so they are virtually always expressed as vectors. Other concepts (such as "mass" and "time") aren't usually associated with any particular direction; so they are virtually always expressed as scalars. Still other concepts (such as "speed" and "length") are sometimes useful with a direction attached, and in other cases useful without a direction; so they may sometimes be expressed as vectors and sometimes not (to emphasize the difference, "speed" is called "velocity" when it has a direction attached; and "length" is called "displacement" when it has a direction attached).

So in summary:

1) The technically correct distinction is: If a quantity is expressed in terms of both a magnitude and a direction, it's a vector; if it's expressed in terms of magnitude only, it's a scalar.

2) In physics, some kinds of quantity are virtually always associated with a direction, and other kinds virtually never are. You can use this fact to get the "right" answer in your workbook, even though (I maintain) the workbook is technically incorrect.

Answer 3

A scalar quantity is any quantity with just a magnitude. A vector quantity has a magnitude and direction. For instance, 2 m/s is a scalar, but 2 m/s north is a vector.

Answer 4

the density is a scalar quantity and a force is a vectorial quantity.Scalar has only a magnitute. a.) this is only speed with magnitute. ,apple,liter (2 miles per hour) are scalars.