Q1.3 Thinking about vectors (T)
Give six examples of physical quantities that are vectors and a further six examples that are scalars.
Identify three respects in which vectors differ from scalars.
Do you think time is a vector or a scalar?
Hint
Reveal

Hint
You should be able to dredge up enough examples from your memory banks. Otherwise you’ll need to browse through HRW, which would be a good thing to do anyway.
The very last bit is to allow you to stretch your imagination a bit.
Solution
Reveal

Solution
Some examples of vectors:
![]() | position |
![]() | velocity |
![]() | force |
![]() | linear momentum |
![]() | angular momentum (could be new to you?) |
![]() | magnetic field (could be new to you?) |
And some scalars …
m | mass |
v | speed |
d | distance |
ρ | density |
R | resistance |
T | temperature |
Some differences between vectors and scalars:
- Well I expect everyone would write down that a vector has a direction associated with it, while a scalar does not.
- A bit more generally you could say that a vector carries more information than a scalar (that’s why it needs 3 numbers to specify a 3D vector, and only one to specify a scalar).
- So when we add vectors together we are really adding together the corresponding components: there are three additions to do for 3D vectors.
- We can multiply vectors together in either of two ways, both of which are quite different from the way we multiply scalars.
- We can never equate a vector to a scalar; any equation that does this is
WRONG. If you write down an equation beginning
then the right hand side must also be a vector which matches the LHS in magnitude and direction.
Is time a vector or a scalar? I put this in to encourage you to muse a little. I’d say it is best thought of as a one-dimensional vector. When we study kinematics we find ourselves using t to label an axis, just like x or y. Though most of us tend to believe we can ‘travel’ only one way along the t-axis!