A scalar quantity can be defined by magnitude alone, but a vector quantity has both magnitude and direction of action. Mass is a scalar quantity because it does not act in any particular direction. The phrase "five kilograms east" is nonsense, indicating the mass cannot be a vector.

Angular momentum, force, displacement, and torque are all vector quantities and describe a value applied in a certain direction.

The largest possible length of the vector sum of the two vectors results when the vectors are oriented in the same direction. In this scenario, the resultant vector will have a length equal to the sum of the magnitudes of the two vectors.

The smallest possible length of the vector sum results when the vectors are oriented in opposite directions. In this scenario, the resultant vector will have a length equal to the different in magnitude between the two vectors.

The largest magnitude of the resultant vector is and the smallest is . Now we need to find the difference between these magnitudes.

Scalar quantities are defined by a magnitude with no applicable direction. In contrast, vector quantities must have both magnitude and direction of action.

Mass, distance, density, and volume are all scalar quantities, simply defined by a magnitude. It impossible to have a directional mass or density, such as "5 kilograms east" or "0.6 grams per liter clockwise." Distance is the scalar form of displacement. Displacement accounts for the direction of a length measurement, while distance measures only the magnitude of the length.

Weight is defined as the force of gravity on an object. All forces are vector quantities.

Scalar quantities are defined by a magnitude with no applicable direction. In contrast, vector quantities must have both magnitude and direction of action.

Distance is a measure of length, taking into account all lengths covered in a path away from a starting point. Displacement is the vector equivalent of distance. Displacement measures length in a given direction from the starting point, without taking into account the path traveled. A car could travel a distance of 400 meters, but if it ultimately returns to its starting position its displacement will be zero.

Velocity is a vector that measure change in displacement per unit time. A force vector, such as weight, results when an acceleration vector (such as gravity) is applied to a mass. Mass itself is a scalar quantity.

Scalar quantities are defined by a magnitude with no applicable direction. In contrast, vector quantities must have both magnitude and direction of action.

The product of a vector quantity and a scalar quantity will always be a vector quantity. Force results from the product of mass (scalar) and acceleration (vector). Weight is a type of force, generated by the acceleration of gravity.

Voltage is a scalar quantity and can be calculated by the product of current (scalar) and resistance (scalar).

Work is a vector quantity and can be calculated by the product of a force (vector) and displacement (vector).

Velocity is a vector and can be calculated by the quotient of displacement (vector) per unit time (scalar).

Scalar quantities are defined by a magnitude with no applicable direction. In contrast, vector quantities must have both magnitude and direction of action.

Speed is defined by a change in distance per unit time. Since distance and time are both scalar quantities, the resulting speed is also scalar. In contrast, velocity is given by a change in displacement per unit time. Since displacement is a vector, the resulting velocity is also a vector. The magnitude of a given speed and given velocity may be equal, but the velocity term will represent the speed applied in a certain direction.

Acceleration is a vector quantity determined by a change in velocity per unit time. Weight is generated by the force of gravity on an object; all forces are vectors.

Scalar quantities are defined by a magnitude with no applicable direction. In contrast, vector quantities must have both magnitude and direction of action.

Some common scalar quantities are distance, speed, mass, and time. Some common vector quantities are force, velocity, displacement, and acceleration.

A vector has both magnitude AND direction, while a scalar just has a magnitude. When asking if something is a vector or a scalar, ask if a direction would make sense -- in this case, force is the only vector. While a direction would help with speed and distance, those are both scalars; the vector version of speed is velocity, and the vector version of distance is displacement.

A scalar quantity can be defined by magnitude alone, while a vector quantity must be defined by both magnitude and direction of action.

Of the given answer options, mass if the only scalar quantity. Mass has magnitude, generally in kilograms, but cannot act in a direction. "7kg west," for example, is nonsensical.

In contrast, displacement, velocity, force, and momentum must be applied in a given direction. Displacement is the vector equivalent of the scalar quantity distance, and velocity is the vector equivalent of the scalar quantity speed. Forces must always act in a given direction, and have no scalar equivalent. Similarly, momentum must always be directional.

There is a distinct and crucial difference between measuring displacement and measuring distance. Distance is a scalar quantity, which means that it depends on the path taken and is independent of the direction traveled. Distance measures the total length traveled, without any reference to the starting point.

In contrast, displacement is a vector quantity. This means that both the magnitude of the length and its direction must be factored into the calculation. Displacement is essentially the net distance traveled in relation to the starting point, independent of the path traveled.

In this question, the skater finishes in exactly the same place that she started. Without any other information, we can conclude that her displacement is zero. It does not matter what path she took to return to her starting point; she could have taken one step forward and one step back, skated the entire rink seventeen times, or simply jumped and landed. All of these possibilities would result in zero displacement.