MHB S6.793.12.4.33 Find the volume of the parallelepiped

[karush]

$\tiny{s6.793.12.4.33}$
$\textsf{
Find the volume of the parallelepiped determined by the vectors, a b and c}$
$ a =\langle 6, 3, -1\rangle
\, b =\langle 0, 1, 2 \rangle
\, c =\langle 4, -2, 5 \rangle $

$\textsf{The volumn of the parallelepiped determined by the vectors }\\$
$\textsf{ $a, b$ and $c$ is the magnitude of their scalar triple product.}$

\begin{align}
\displaystyle
V&=|a \cdot(b \times c)|\\
\end{align}
then
\begin{align}
V=|a \cdot(b \times c)|&=
\begin{bmatrix}
6 & 3 & -1\\
0 &1 &2\\
4 &-2 &5
\end{bmatrix} \\
&=6\begin{bmatrix}=
1 &2\\
-2 &5
\end{bmatrix}
+3\begin{bmatrix}
0 &2\\
4 &5
\end{bmatrix}
-\begin{bmatrix}
0 &1\\
4 &-2
\end{bmatrix}\\
&= 6(9)-3(-8) +(4) \\
&\color{red}{V=82}
\end{align}
$\textit{ok think this is ok. but always suggestions! }\\$
$\textit{btw need more lines to expand to in latex window scrolling constantly not fun}$

 

[Joppy]

Looks good to me. A few errors in transferring your notes to here, but i think you have understood the process.

btw need more lines to expand to in latex window scrolling constantly not funbtw need more lines to expand to in latex window scrolling constantly not fun

I agree! There is a little tab down the bottom right of the text window that you can pull to increase the size.

EDIT: Ohh that window... I didn't even know it was there :). I usually just type in the big window and then hit preview to check my LaTeX.

 

[karush]

\begin{align}
V=|a \cdot(b \times c)|&=
\begin{bmatrix}
6 & 3 & -1\\
0 &1 &2\\
4 &-2 &5
\end{bmatrix} \\
&=6\begin{bmatrix}
1 &2\\
-2 &5
\end{bmatrix}
+3\begin{bmatrix}
0 &2\\
4 &5
\end{bmatrix}
-\begin{bmatrix}
0 &1\\
4 &-2
\end{bmatrix}\\
&=6(9)-3(-8) +(4) \\
&=\color{red}{82}
\end{align}
$\textit{think this is it. well the expand tab doesn't work on a tablet! }$

 

[Joppy]

Looks better :)

$\textit{think this is it. well the expand tab doesn't work on a tablet! }$

True.. I just tried on my iPad and it doesn't work. I guess we'll just have to be more concise with our posts xD.