# Vector inner product and cross product Calculator

## Calculates the inner product and the cross product of two vectors.

 $inner\ product:\ {\bf a}\cdot {\bf b}\\\hspace{50}{\bf a}\cdot {\bf b}=\sum_{i=1}^{n}a_i b_i=c\\\vspace{5}cross\ product:\ {\bf a}\times {\bf b}\\\hspace{50}{\bf a}\times {\bf b}=\normal{\left(\begin{array}\vspace{10} a_1\\\vspace{10} a_2\vspace{20}\\a_3\\\end{array}\right)} \times \normal{\left(\begin{array}\vspace{10} b_1\\\vspace{10} b_2\vspace{20}\\b_3\\\end{array}\right)} =\normal{\left(\begin{array}\vspace{10} a_2 b_3 -a_3 b_2\\\vspace{10} a_3 b_1 -a_1 b_3\vspace{20}\\a_1 b_2 -a_2 b_1\\\end{array}\right)}=\large {\bf c}\\$

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 The inner product "ab" of a vector can be multiplied only if "a vector" and "b vector" have the same dimension.The outer product "a × b" of a vector can be multiplied only when "a vector" and "b vector" have three dimensions.$inner\ product:\ {\bf a}\cdot {\bf b}=c\ :scalar\\cross\ product:\ {\bf a}\times {\bf b}={\bf c}\ :vector\\$

Vector inner product and cross product
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