Karlee Rivas

2023-03-09

What is the value of $\left(A$x$B{\right)}^{2}$ + ${\left(A\cdot B\right)}^{2}$?

Given explanation: $|A×B|=|A||B|\mathrm{sin}\varphi$
$|A\cdot B|=|A||B|\mathrm{cos}\varphi$
here $\varphi$ is the angle between $A$ and $B$ at common tails.
then
${|A×B|}^{2}+{|A\cdot B|}^{2}={|A|}^{2}{|B|}^{2}\left({\mathrm{sin}}^{2}\varphi +{\mathrm{cos}}^{\varphi }\right)={|A|}^{2}{|B|}^{2}$

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