- #1

karush

Gold Member

MHB

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$\tiny{s6.793.12.4.33}$

$\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}

$\textit{ok think this is ok. but always suggestions! }\\$

$\textit{btw need more lines to expand to in latex window scrolling constantly not fun}$

$\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}

$\textit{ok think this is ok. but always suggestions! }\\$

$\textit{btw need more lines to expand to in latex window scrolling constantly not fun}$

Last edited: