Back to Exercise: Recognize and represent vector quantities

Exercises: Recognize and Represent Vector Quantities

Work through each section in order. For multiple-choice problems, select the best answer. For short-response problems, write a complete explanation.

Grade 9·20 problems·~30 min·Common Core Math - HS Number and Quantity·standard·hsn-vm-a-1

Printable layout

Recall / Warm-Up

Which of the following quantities is a vector quantity?

Temperature: 72 degrees F

Mass: 5 kg

Velocity: 60 mph due north

Speed: 60 mph

A vector is drawn as a directed line segment from point $A$ to point $B$ . Which end of the segment has the arrowhead?

Point $A$ , the starting end

Point $B$ , the ending end

Both ends

The middle of the segment

Which of the following is NOT a valid notation for a vector?

$\mathbf{v}$ (boldface letter)

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

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

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

Fluency Practice

A weather report states: "Wind speed is 25 mph." Is this a complete description of the wind as a vector quantity?

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.

Which pair of quantities correctly classifies each as scalar or vector?

Distance: scalar; Displacement: vector

Distance: vector; Displacement: scalar

Distance: scalar; Displacement: scalar

Distance: vector; Displacement: vector

A vector is drawn as a directed line segment from $P(2, 1)$ to $Q(5, 4)$ . Which statement is correct?

$P$ 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.

Arrow $\mathbf{u}$ starts at $(0, 0)$ and ends at $(3, 2)$ . Arrow $\mathbf{w}$ starts at $(4, 1)$ and ends at $(7, 3)$ . Are $\mathbf{u}$ and $\mathbf{w}$ equal vectors?

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 expression $|\mathbf{v}|$ represents which of the following?

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

You're viewing 2 of 6 sections.

Create a free account to continue the full exercise set and save your progress.

Create free account