Understanding Vector Quantities and Representation - Pre-Calculus
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What is the name of the point where a vector begins on a directed segment: initial point, terminal point, or midpoint?
What is the name of the point where a vector begins on a directed segment: initial point, terminal point, or midpoint?
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Initial point (tail). Vectors start at the tail (initial point).
Initial point (tail). Vectors start at the tail (initial point).
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What is the name of the point where a vector ends on a directed segment: initial point, terminal point, or midpoint?
What is the name of the point where a vector ends on a directed segment: initial point, terminal point, or midpoint?
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Terminal point (head). Vectors end at the head (terminal point).
Terminal point (head). Vectors end at the head (terminal point).
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Identify the correct statement: $|\vec{v}|$ can be negative, or $|\vec{v}|\ge 0$ always.
Identify the correct statement: $|\vec{v}|$ can be negative, or $|\vec{v}|\ge 0$ always.
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$|\vec{v}|\ge 0$ always. Magnitude is a distance, never negative.
$|\vec{v}|\ge 0$ always. Magnitude is a distance, never negative.
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What is the magnitude of the zero vector $\vec{0}$?
What is the magnitude of the zero vector $\vec{0}$?
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$|\vec{0}|=0$. Zero vector has no length.
$|\vec{0}|=0$. Zero vector has no length.
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Which option best describes the direction of the zero vector $\vec{0}$: defined or undefined?
Which option best describes the direction of the zero vector $\vec{0}$: defined or undefined?
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Undefined direction. Zero vector points nowhere (no direction).
Undefined direction. Zero vector points nowhere (no direction).
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What does it mean for two vectors $\vec{u}$ and $\vec{v}$ to be equal using directed segments?
What does it mean for two vectors $\vec{u}$ and $\vec{v}$ to be equal using directed segments?
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Same magnitude and same direction (even if located in different places). Equal vectors are parallel with same length.
Same magnitude and same direction (even if located in different places). Equal vectors are parallel with same length.
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What does it mean for vectors $\vec{u}$ and $\vec{v}$ to have the same magnitude but different directions?
What does it mean for vectors $\vec{u}$ and $\vec{v}$ to have the same magnitude but different directions?
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$|\vec{u}|=|\vec{v}|$ but $\vec{u}\ne\vec{v}$ due to direction. Same length but pointing different ways.
$|\vec{u}|=|\vec{v}|$ but $\vec{u}\ne\vec{v}$ due to direction. Same length but pointing different ways.
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Identify the correct relationship between $\vec{v}$ and $-\vec{v}$ regarding magnitude and direction.
Identify the correct relationship between $\vec{v}$ and $-\vec{v}$ regarding magnitude and direction.
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$|\vec{v}|=|-\vec{v}|$ and directions are opposite. Negative reverses direction, keeps length.
$|\vec{v}|=|-\vec{v}|$ and directions are opposite. Negative reverses direction, keeps length.
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Find the magnitude of the vector $\vec{v}=\langle 3,4\rangle$.
Find the magnitude of the vector $\vec{v}=\langle 3,4\rangle$.
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$|\vec{v}|=5$. Use Pythagorean theorem: $\sqrt{3^2+4^2}=5$.
$|\vec{v}|=5$. Use Pythagorean theorem: $\sqrt{3^2+4^2}=5$.
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What is a standard geometric way to represent a vector in the plane?
What is a standard geometric way to represent a vector in the plane?
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As a directed line segment (an arrow). The arrow shows both length (magnitude) and direction.
As a directed line segment (an arrow). The arrow shows both length (magnitude) and direction.
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Which option is a scalar quantity: velocity, force, acceleration, or speed?
Which option is a scalar quantity: velocity, force, acceleration, or speed?
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Speed. Speed is just a number; velocity includes direction too.
Speed. Speed is just a number; velocity includes direction too.
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Which option is a vector quantity: mass, temperature, displacement, or time?
Which option is a vector quantity: mass, temperature, displacement, or time?
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Displacement. Displacement has direction; mass, temperature, and time don't.
Displacement. Displacement has direction; mass, temperature, and time don't.
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What is the defining feature of a scalar quantity?
What is the defining feature of a scalar quantity?
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A scalar has magnitude only (no direction). Unlike vectors, scalars don't point in any direction.
A scalar has magnitude only (no direction). Unlike vectors, scalars don't point in any direction.
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What is the defining feature that makes a quantity a vector rather than a scalar?
What is the defining feature that makes a quantity a vector rather than a scalar?
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A vector has both magnitude and direction. Scalars like temperature have only size, not direction.
A vector has both magnitude and direction. Scalars like temperature have only size, not direction.
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What is the magnitude notation for the vector $\overrightarrow{AB}$?
What is the magnitude notation for the vector $\overrightarrow{AB}$?
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$|\overrightarrow{AB}|$. Apply magnitude bars to get the distance from $A$ to $B$.
$|\overrightarrow{AB}|$. Apply magnitude bars to get the distance from $A$ to $B$.
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Identify whether $|\vec{v}|$ is a vector or a scalar.
Identify whether $|\vec{v}|$ is a vector or a scalar.
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Scalar. Magnitudes are non-negative numbers without direction.
Scalar. Magnitudes are non-negative numbers without direction.
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Which statement is correct: $|\vec{v}|$ can be negative, or $|\vec{v}| \ge 0$ always?
Which statement is correct: $|\vec{v}|$ can be negative, or $|\vec{v}| \ge 0$ always?
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$|\vec{v}| \ge 0$ always. Magnitude represents length, which cannot be negative.
$|\vec{v}| \ge 0$ always. Magnitude represents length, which cannot be negative.
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What is $|\vec{0}|$, where $\vec{0}$ is the zero vector?
What is $|\vec{0}|$, where $\vec{0}$ is the zero vector?
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$0$. The zero vector has no length in any direction.
$0$. The zero vector has no length in any direction.
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Identify the meaning of $|\vec{v}|$ in one phrase.
Identify the meaning of $|\vec{v}|$ in one phrase.
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The magnitude (length) of $\vec{v}$. Double bars also convert a vector to its scalar length.
The magnitude (length) of $\vec{v}$. Double bars also convert a vector to its scalar length.
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Identify the meaning of $|\vec{v}|$ in one phrase.
Identify the meaning of $|\vec{v}|$ in one phrase.
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The magnitude (length) of $\vec{v}$. The bars convert a vector to its scalar length.
The magnitude (length) of $\vec{v}$. The bars convert a vector to its scalar length.
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What is the tail of a directed segment representing a vector?
What is the tail of a directed segment representing a vector?
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The starting point of the arrow. The arrow points from tail to head.
The starting point of the arrow. The arrow points from tail to head.
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What is the head of a directed segment representing a vector?
What is the head of a directed segment representing a vector?
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The endpoint (arrow tip). The arrow points from tail to head.
The endpoint (arrow tip). The arrow points from tail to head.
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What is the magnitude of a vector represented by a directed segment?
What is the magnitude of a vector represented by a directed segment?
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The length of the directed segment. Longer arrows represent vectors with greater magnitude.
The length of the directed segment. Longer arrows represent vectors with greater magnitude.
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What notation is commonly used to denote a vector $v$ (choose one standard symbol form)?
What notation is commonly used to denote a vector $v$ (choose one standard symbol form)?
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$\vec{v}$. The arrow over $v$ indicates it's a vector quantity.
$\vec{v}$. The arrow over $v$ indicates it's a vector quantity.
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What alternative notation also represents the magnitude of a vector $\vec{v}$?
What alternative notation also represents the magnitude of a vector $\vec{v}$?
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$|\vec{v}|$. Double bars are another way to denote vector length.
$|\vec{v}|$. Double bars are another way to denote vector length.
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What symbol denotes the vector from point $A$ to point $B$?
What symbol denotes the vector from point $A$ to point $B$?
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$\overrightarrow{AB}$. The arrow indicates direction from first to second point.
$\overrightarrow{AB}$. The arrow indicates direction from first to second point.
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Which option is the correct notation for the vector from point $A$ to point $B$: $\overrightarrow{AB}$ or $\overrightarrow{BA}$?
Which option is the correct notation for the vector from point $A$ to point $B$: $\overrightarrow{AB}$ or $\overrightarrow{BA}$?
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$\overrightarrow{AB}$. Order matters: from $A$ to $B$.
$\overrightarrow{AB}$. Order matters: from $A$ to $B$.
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Find the magnitude of the vector $\vec{v}=\langle -6,8\rangle$.
Find the magnitude of the vector $\vec{v}=\langle -6,8\rangle$.
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$|\vec{v}|=10$. Apply $|\vec{v}|=\sqrt{(-6)^2+8^2}=\sqrt{100}$.
$|\vec{v}|=10$. Apply $|\vec{v}|=\sqrt{(-6)^2+8^2}=\sqrt{100}$.
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Identify whether each is a vector or scalar: displacement, speed, velocity, temperature.
Identify whether each is a vector or scalar: displacement, speed, velocity, temperature.
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Vectors: displacement, velocity; scalars: speed, temperature. Vectors have direction; scalars don't.
Vectors: displacement, velocity; scalars: speed, temperature. Vectors have direction; scalars don't.
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What is a directed line segment representation of a vector (what do the endpoints indicate)?
What is a directed line segment representation of a vector (what do the endpoints indicate)?
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A segment with an arrow from initial point (tail) to terminal point (head). Arrow points from starting to ending position.
A segment with an arrow from initial point (tail) to terminal point (head). Arrow points from starting to ending position.
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