Dot Product of Parallel Vectors
Dot product is the product of magnitude of the two vectors with cosine of the angle between the two vectors. For parallel vectors the angle between the two vectors is 0°. So dot product of parallel vectors is simply the product of their magnitudes.
By definition of dot product of two vectors we know that,
a.b =|a| |b| cosθ
As angle between parallel vectors is zero,
a.b = |a| |b| cos0
a.b = |a| |b| (1)
a.b = |a| |b|
Hence it is proved that the dot product of two parallel vectors is the product of their magnitudes.
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.
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