Scalar quantities give a magnitude, while vector quantities give a magnitude and a direction. The answer will be a measurement that does not change, regardless of the direction of action.

Displacement is a measure of length in a given direction; distance is the scalar version of displacement.

Velocity is a measure of rate in a given direction; speed is the scalar version of velocity.

Force is a derivative of acceleration, and can only act in a given direction. There is no scalar equivalent of force. Similarly, momentum is a derivative of velocity and has no scalar equivalent.

Mass is a measure solely of magnitude, and requires no direction of action. Mass is a scalar quantity.

A vector has both magnitude and direction, while a scalar has only magnitude. Ask yourself, "for which of these things is there a direction?" For displacement, we would say "50 meters NORTH," whereas with the others, we would say "50 meters," "20 seconds," or "30 miles per hour."

Important distinctions to know:

Speed is a scalar, while velocity is a vector.

Distance is a scalar, while displacement is a vector.

Force and acceleration are vectors. Time is a scalar.

The difference between a scalar and a vector is that a vector requires a direction. Scalar quantities have only magnitude; vector quantities have both magnitude and direction. Time is completely separated from direction; it is a scalar. It has only magnitude, no direction.

Force, displacement, and acceleration all occur with a designated direction.

Important distinctions to know:

Speed is a scalar, while velocity is a vector.

Distance is a scalar, while displacement is a vector.

Force and acceleration are vectors. Time is a scalar.

Distance is a scalar quantity and will take into account only the number of floors travelled, regardless of the direction of movement.

Walter takes an incredibly complicated path to wash the windows on the building. When calculating distance, we add up all the movement he does, regardless of direction.

First, he travels down one floor (4th to 3rd).

Then he travels up three floors (3rd to 6th).

Then he travels down one floor (6th to 5th), then down another three floors (5th to 2nd).

Finally, he travels down one more floor (2nd to 1st).

In total, Walter travelled .

When multiplying a vector by a constant (called scalar multiplication), we multiply each component by the constant.

The magnitude of this new vector is found with these new components:

To calculate the angle we must first find the inverse tangent of :

This is the principal arctan, but it is in the first quadrant while our vector is in the third. We to add the angle 180° to this value to arrive at our final answer.

Finding the resultant requires us to add like components:

Vector quantities have both magnitude and direction, while scalar quantities have only magnitude.

Velocity, acceleration, force, and displacement are all vectors. They must have a magnitude, as well as a direction of action. A velocity can be to the north, and a displacement can be east. A good way to identify vectors is if they can be negative. A negative vector indicates "downward" or "to the left," while a negative scalar cannot exist.

Volume is not a vector; it cannot have a direction. An object cannot have a volume of to the left, not can it have a volume of .

Unlike displacement, which only measures the change between starting point and ending point, distance measures the entire trip travelled. Displacement is a vector, while distance is a scalar; thus, displacement is independent of path, while distance is dependent on path.

Each circuit the dog travels a total of , and he makes this trip eight times.

He will travel a total distance of .

The total displacement would be zero because the dog's ending position does not change, relative to his starting position.

Vector quantities are defined by both the magnitude of the parameter and the direction of action. In contract, scalar quantities are independent of direction and rely only on the magnitude of the parameter.

Mass, distance, time, and brightness are all scalar quantities. This is to say that none of these terms can be applied in a given direction. It would be illogical to have "three grams west" or "eighteen seconds to the left." Distance is the scalar equivalent of the displacement vector.

Force is always a vector quantity, since the direction of the force matters in defining the parameter. "Four Newtons to the right" is quantifiably different from "four Newtons downward" or "four Newtons to the left."

A vector quantity is described by both its magnitude, and its direction of action. In contrast, a scalar quantity is described only by its magnitude.

Force is a vector because the direction of action is relevant to describing the force. An upward force is notably different from a downward force.

Voltage, resistance, charge, and electric potential are scalar quantities and are the same regardless of any direction of action. For example, turning a circuit sideways does not alter the values for any of these quantities.