Dot Product of Unit Vectors
A unit vector is a vector with a magnitude of 1.
The dot product of two unit vectors simplifies to the cosine of the angle between them because the magnitude terms (|a| and |b|) in the formula become 1.
Dot Product
Dot Product, a fundamental operation in mathematics, is a unique way of combining two vectors that results in a scalar. This operation, often symbolized by a centered dot, is dependent on the length of both vectors and the angle between them.
Intuitively, the Dot Product tells us how much two vectors point in the same direction. It essentially measures the relative direction of two vectors. When the angle between the vectors is small, indicating they point in a similar direction, the dot product is large. Conversely, when the vectors are perpendicular, the dot product is zero.
In the following sections of this article, we will delve deeper into the concept of dot product, exploring its algebraic and geometric definitions, properties, and applications in various fields.
Table of Content
- What is Dot Product?
- Formula of Dot Product
- Angle Between Two Vectors Using Dot Product
- Projection of a Vector
- Working Rule to Find The Dot Product of Two Vectors
- Matrix Representation of Dot Product
- Dot Product of Unit Vectors
- Properties of Dot Product
- Applications of Dot Product
- Solved Examples on Dot Product
- Practice Problems on Dot Product