Here we will quickly find out the concepts behind the scalar product and the vector product with their fundamental difference. Also, we will site very common examples of the scalar product and vector product. (one for each type of product).
There are two kinds of products of vectors used broadly in physics and engineering.
What is a scalar product or dot product? Give one example
One kind of multiplication is a scalar multiplication of two vectors.
A scalar product of two vectors results in a number (a scalar), as its name indicates. It is also known as the dot product, as the dot(.) symbol is used to denote this type of product.
An Example of the scalar product or dot product
Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector.
That’s why work is considered as a scalar quantity.
[ Read: Scalar Product formula and sample problem solving ]
What is a vector product or cross product?
A quite different kind of multiplication is a vector multiplication of vectors.
Taking a vector product of two vectors returns a vector as a result, as its name suggests. Vector products are used to define other derived vector quantities. It is also known as Cross Product, as the cross (x) symbol is used to denote this type of product.
An example of Vector Product or Cross Product
An Example of the vector product: For example, in describing rotations, a vector quantity called torque is defined as a vector product of an applied force (a vector) and the perpendicular distance from the pivot to force (a vector).
The fundamental difference between the scalar product and vector product:
It is important to distinguish between these two kinds of vector multiplications because the scalar product is a scalar quantity and a vector product is a vector quantity.