Karlee Rivas

2023-03-09

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

Aaliyah Padilla

Beginner2023-03-10Added 10 answers

Given explanation: $\left|A\times B\right|=\left|A\right|\left|B\right|\mathrm{sin}\varphi$

$\left|A\cdot B\right|=\left|A\right|\left|B\right|\mathrm{cos}\varphi$

here $\varphi$ is the angle between $A$ and $B$ at common tails.

then

$\left|A\times B\right|}^{2}+{\left|A\cdot B\right|}^{2}={\left|A\right|}^{2}{\left|B\right|}^{2}({\mathrm{sin}}^{2}\varphi +{\mathrm{cos}}^{\varphi})={\left|A\right|}^{2}{\left|B\right|}^{2$

$\left|A\cdot B\right|=\left|A\right|\left|B\right|\mathrm{cos}\varphi$

here $\varphi$ is the angle between $A$ and $B$ at common tails.

then

$\left|A\times B\right|}^{2}+{\left|A\cdot B\right|}^{2}={\left|A\right|}^{2}{\left|B\right|}^{2}({\mathrm{sin}}^{2}\varphi +{\mathrm{cos}}^{\varphi})={\left|A\right|}^{2}{\left|B\right|}^{2$