What is the difference between a vector and a scalar?

Question

a
A vector measurement is required for distance, a scalar measurement is required for displacement
b
A vector is only used in measuring forces, a scalar is only used in measuring mass
c
A vector is only measured in SI units, where scalars are only measured in US Customary units
d
A vector measurement contains a direction and magnitude, a scalar measurement only contains a magnitude

Answer 1

The correct answer is:

d A vector measurement contains a direction and magnitude, a scalar measurement only contains a magnitude.

Vectors represent quantities that have both a magnitude and a direction (e.g., velocity, force), while scalars are quantities that have only magnitude and no direction (e.g., temperature, mass).

Answer 2

A radioisotope has a half-life of 7.5 hours. How many half lives have occured after 67.5 hours?

a
7 half-lives
b
8 half-lives
c
9 half-lives
d
10 half-lives

Answer 3

To determine how many half-lives have occurred after 67.5 hours for a radioisotope with a half-life of 7.5 hours, you can divide the total time by the half-life:

\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{67.5 \text{ hours}}{7.5 \text{ hours}} = 9 \]

Thus, the correct answer is:

c 9 half-lives.