Question

What does a dot product equal to $1$ mean?

Answer 1

Properties of dot product:

Dot product is also known as scalar product of two vectors and it is represented as $\overrightarrow{\mathbf{A}}\mathbf{.}\overrightarrow{\mathbf{B}}\mathbf{=}\mathit{A}\mathit{B}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{\theta }$, where $\overrightarrow{A,}\overrightarrow{B}$are vectors and $A,B$ represent magnitude of vectors and $\theta$ is angle between the vectors.

If the dot product of two vectors is $1$ then,

1. The vectors are in the same direction and it is given that vectors are unit vectors..
2. If vectors are in the same direction then vectors lengths are reciprocals of each other.

Hence, meaning of dot product is 1 defined.