Scalar quantity is a quantity with magnitude.

Vector quantity is a quantity with both magnitude and direction.

# Tag Archives: vector

## Work Done, Energy and Power are Scalar Quantities

**Work Done, Kinetic Energy (KE), Gravitational Potential Energy (GPE) and Power are all SCALAR quantities.**

Many have asked if Work Done is scalar or vector? Though from our textbook, **Work Done = Force x distance in the direction of the forc**e.

In other words, **Work Done = Force x Displacement**

We already know that **Force is a vector**. Weight being a force, is also a vector quantity. Displacement is distance in a specific direction, hence it is a vector quantity too. In tertiary education, you will learn in details that the **product (multiplication) of two vectors will result in a scalar or dot product**.

Since it is out of syllabus, it will be good to use other ways to help you to understand and recall.

Method 1 Remember vector x vector will end up a scalar. Similar to (-)x(-) = (+) Method 2 Consider moving a box up to a certain height, work done or gain in GPE is constant regardless of the path it takes (diagonal or vertical). Hence direction is not important, therefore **GPE is a scalar**.

When considering KE, since **KE = 1/2mv ^{2}** , similar to Method 1, v

^{2}is actually velocity x velocity. Hence it product of 2 vectors, resulting in

**KE being a scalar**.

**Power = Energy Conversion/ time** or **Work Done / time**,

since energy, work done and time are scalar, **Power is a scalar quantity**.

* Other important note:* Power = Rate of work done = Rate of energy conversion.

## Work Done, Energy and Power are Scalar Quantities

**Work Done, Kinetic Energy (KE), Gravitational Potential Energy (GPE) and Power are all SCALAR quantities.**

Many have asked if Work Done is scalar or vector? Though from our textbook, **Work Done = Force x distance in the direction of the forc**e.

In other words, **Work Done = Force x Displacement**

We already know that **Force is a vector**. Weight being a force, is also a vector quantity. Displacement is distance in a specific direction, hence it is a vector quantity too. In tertiary education, you will learn in details that the **product (multiplication) of two vectors will result in a scalar or dot product**.

Since it is out of syllabus, it will be good to use other ways to help you to understand and recall.

Method 1 Remember vector x vector will end up a scalar. Similar to (-)x(-) = (+) Method 2 Consider moving a box up to a certain height, work done or gain in GPE is constant regardless of the path it takes (diagonal or vertical). Hence direction is not important, therefore **GPE is a scalar**.

When considering KE, since **KE = 1/2mv ^{2}** , similar to Method 1, v

^{2}is actually velocity x velocity. Hence it product of 2 vectors, resulting in

**KE being a scalar**.

**Power = Energy Conversion/ time** or **Work Done / time**,

since energy, work done and time are scalar, **Power is a scalar quantity**.

* Other important note:* Power = Rate of work done = Rate of energy conversion.