- #1
greg_rack
Gold Member
- 363
- 79
- Homework Statement
- Derive the formula for calculating: ##\vec{U}\times \vec{B}##
- Relevant Equations
- none
Writing both ##\vec{U}## and ##\vec{B}## with magnitude in all the three spatial coordinates:
$$
\vec{U}\times \vec{B}=
(U_{x}\cdot \widehat{i}+U_{y}\cdot \widehat{j}+U_{z}\cdot \widehat{k})\times
(B_{x}\cdot \widehat{i}+B_{y}\cdot \widehat{j}+B_{z}\cdot \widehat{k})$$
From this point on, I cannot understand the calculations needed to obtain the final formula:
$$
\vec{U}\times \vec{B}=
\widehat{i}(U_{y}B_{z}-U_{z}B_{y})... $$
$$
\vec{U}\times \vec{B}=
(U_{x}\cdot \widehat{i}+U_{y}\cdot \widehat{j}+U_{z}\cdot \widehat{k})\times
(B_{x}\cdot \widehat{i}+B_{y}\cdot \widehat{j}+B_{z}\cdot \widehat{k})$$
From this point on, I cannot understand the calculations needed to obtain the final formula:
$$
\vec{U}\times \vec{B}=
\widehat{i}(U_{y}B_{z}-U_{z}B_{y})... $$