Properties of Parallel Vectors
Some of the Important properties of Parallel vectors are as below:
- Every vector is parallel to itself and antiparallel to its opposite.
- Parallel vector lie on the same or parallel lines.
- Cross product of parallel vectors is always zero.
- Sum of two parallel vectors is also a parallel vector.
- Dot product of two parallel vectors is equal to the product of their magnitudes.
- Two vectors are parallel if they can be represented as scalar multiple of one another.
Parallel Vector
Parallel vectors are considered one of the most important concepts in vector algebra. When two vectors have the same or opposite direction, they are said to be parallel to each other. Note that parallel vectors can differ in magnitude, and two parallel vectors can never intersect each other. They are widely used in mathematics, physics, and other areas of engineering for defining lines and planes, representing force and velocity, and analyzing various structures.
In this article, we will learn about parallel vectors, the dot product, and the cross product of parallel vectors, as well as their properties, in detail.