Exercises: Recognize and Represent Vector Quantities

Temperature: 72 degrees F

Mass: 5 kg

Velocity: 60 mph due north

Speed: 60 mph

Point $A$, the starting end

Point $B$, the ending end

Both ends

The middle of the segment

$\mathbf{v}$ (boldface letter)

$\vec{v}$ (letter with arrow)

$\overrightarrow{AB}$ (directed from $A$ to $B$)

$|\mathbf{v}|$ (bars around a bold letter)

Yes — it gives the magnitude of the wind.

No — it gives speed (magnitude) but no direction; a vector requires both.

Yes — wind always blows in one direction, so direction is implied.

No — mph is not a valid unit for vectors.

Distance: scalar; Displacement: vector

Distance: vector; Displacement: scalar

Distance: scalar; Displacement: scalar

Distance: vector; Displacement: vector

$P$ is the terminal point and $Q$ is the initial point.

$P$ is the initial point and $Q$ is the terminal point.

Both $P$ and $Q$ are terminal points.

The initial point must be at the origin.

No — they start at different points, so they are different vectors.

Yes — they have the same length and direction, so they are equal vectors.

No — one starts at the origin and the other does not.

Yes — all arrows of the same length are equal.

The vector $\mathbf{v}$ itself

The magnitude (length) of vector $\mathbf{v}$, a non-negative scalar

The negative of vector $\mathbf{v}$

The absolute value of a negative number