Question

What are cross product and dot product?

Answer 1

Step-1:Cross product:

• Cross product is a binary operation on two vectors in three-dimensional space.
• The resultant vector of the cross product is perpendicular to both vectors.
• It is also called the vector product.
• The cross product of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

$\overrightarrow{\mathbf{A}}\mathbf{\times }\overrightarrow{\mathbf{B}}\mathbf{=}\left|\overrightarrow{A}\right|\left|\overrightarrow{B}\right|\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }\hat{\mathbf{\eta }}$ , where $\left|\overrightarrow{A}\right|,\left|\overrightarrow{B}\right|$ are the magnitudes of the vectors and $\theta$ is the angle between the vectors and $\hat{\eta }$ is vector perpendicular to both vectors.

Step-2: Dot product:

• The dot product is a scalar number obtained by performing a specific operation on the vector components.
• It is also called the scalar product.
• The dot product of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

$\overrightarrow{\mathbf{A}}\mathbf{·}\overrightarrow{\mathbf{B}}\mathbf{=}\left|\overrightarrow{A}\right|\left|\overrightarrow{B}\right|\mathit{c}\mathit{o}\mathit{s}\mathit{\theta }$ , where $\left|\overrightarrow{A}\right|,\left|\overrightarrow{B}\right|$ are the magnitudes of the vectors and $\theta$ is the angle between the vectors.