# Scalar product formula with an example

Last updated on April 14th, 2021 at 05:17 pm

**Scalar multiplication of two vectors yields a scalar product. Scalar multiplication is also known as the dot product.** In the next section, we will see how the **scalar product formula** or equation is written.

**Scalar product formula** | equation of dot product

**The scalar product of 2 vectors A and B is expressed by the following equation:A.B = AB cos φ, where φ is the angle between the vectors, A is the magnitude of vector A and B is the magnitude of vector B.**

**The scalar product is also called the dot product because of the dot notation that indicates it.**

In figure (b), vector A is projected along the direction of vector B, as a result, a projected component of vector **A** is generated along the direction of vector **B**. And this component is *A cos φ*.

Similarly, in figure (c), the vector B is projected along the direction of vector A, as a result, a projected component of vector B is generated along the direction of vector **A**. And this component is *B cos φ*.

In both cases, you can see how the **cos φ** is generated as we are working to find out a scalar product of 2 vectors **A** and **B**.

## Numerical problem solving using the scalar product or dot product

**Two vectors A and F are shown in the above 2 diagrams. Find the scalar or dot product of A and F.**

**Solution**

From Figure, the magnitudes of vectors **A** and **F** are A = 10.0 and F = 20.0.

Angle θ , between them, is the difference: θ = φ − α = 110° − 35° = 75° .

Substituting these values into Equation of scalar product gives the scalar product.

A straightforward calculation gives us **A.F =** AF cos θ = (10.0)(20.0) cos 75° = 51.76.

## Work is scalar or vector?

Work is a scalar. It’s a scalar product of 2 vectors, force, and displacement. As work is scalar, only the Magnitude of work counts.

## Energy is scalar or vector?

Energy is a scalar. only the Magnitude of energy counts.

## Power is scalar or vector?

Power is a scalar quantity. It has no direction attached. Magnitude of power only matters.