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Vector dot product and cross product

TOP/Linear Algebra/Vector
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Calculates the dot product and cross product between two vectors.
\(inner\ product:\ {\bf a}\cdot {\bf b}\\ \hspace{50px}{\bf a}\cdot {\bf b}=\displaystyle \sum_{i=1}^{n}a_i b_i=c\\ cross\ product:\ {\bf a}\times {\bf b}\\ \hspace{50px}{\bf a}\times {\bf b}=\normalsize{\left(\begin{array}\\ a_1\\ a_2\\a_3\\\end{array}\right)} \times \normalsize{\left(\begin{array}\\ b_1\\ b_2\\b_3\\\end{array}\right)} =\normalsize{\left(\begin{array}\\ a_2 b_3 -a_3 b_2\\ a_3 b_1 -a_1 b_3\\a_1 b_2 -a_2 b_1\\\end{array}\right)}=\large {\bf c}\\ \)
(Click the bottom row of each vector to enter a value)
vector
a1
a2
a3
vector
b1
b2
b3
The dot product ab of vectors can only be calculated when a and b have the same dimension.
The cross product a×b of vectors can only be calculated when a and b are three-dimensional.

\(inner\ product:\ {\bf a}\cdot {\bf b}=c\ :scalar\\ cross\ product:\ {\bf a}\times {\bf b}={\bf c}\ :vector\\\)

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