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\displaystyle{\vec{a}^\star = \frac{\vec{b}\times \vec{c}}{\vec{a}\cdot\left( \vec{b}\times\vec{c} \right)} = \frac{\left(\begin{array}{c}[br]bc\\[br]0\\[br]0\end{array}\right)}{abc} = \left(\begin{array}{c}[br]1/a\\[br]0\\[br]0\end{array}\right)}
\displaystyle{\vec{b}^\star =\left(\begin{array}{c}[br]0\\[br]1/b\\[br]0\end{array}\right)}
\displaystyle{\vec{c}^\star = \left(\begin{array}{c}[br]0\\[br]0\\[br]1/c\end{array}\right)}
\displaystyle\vec{g} = h \left(\begin{array}{c}[br]1/a\\[br]0\\[br]0\end{array}\right) + k \left(\begin{array}{c}[br]0\\[br]1/b\\[br]0\end{array}\right) + l \left(\begin{array}{c}[br]0\\[br]0\\[br]1/c\end{array}\right) = \left(\begin{array}{c}[br]h/a\\[br]k/b\\[br]l/c\end{array}\right)}
\displaystyle\vec{r} = \left(\begin{array}{c}[br]a/h\\[br]0\\[br]0\end{array}\right) +x \left(\begin{array}{c}[br]a/h\\[br]-b/k\\[br]0\end{array}\right) + y \left(\begin{array}{c}[br]a/h\\[br]0\\[br]-c/l\end{array}\right)}
\displaystyle\vec{r} = \left(\begin{array}{c}[br]a/h+ax/h + ay/h\\[br]-bx/k\\[br]-cy/l\end{array}\right)}
\displaystyle{\begin{aligned}\vec{r}\cdot\vec{g} & = \left(\begin{array}{c}[br]a/h+ax/h + ay/h\\[br]-bx/k\\[br]-cy/l\end{array}\right) \cdot \left(\begin{array}{c}[br]h/a\\[br]k/b\\[br]l/c\end{array}\right) = \\ [br]& = - x - y + \frac{h}{a} \left( a/h + (a x)/h + (a y)/h \right) \\ [br]& = - x - y+1+x+y \\ & =1[br]\end{aligned}}
Last reply 1 week ago
Im confused about this chemistry question, why does it form these productsLast reply 1 week ago
Im confused about this chemistry question, why does it form these products