Two adjacent sides of a parallelogram are represented by the two vectors $\hat i + 2\hat j + 3\hat k$ and $3\hat i - 2\hat j + \hat k$. What is the area of parallelogram
Two adjacent sides of a parallelogram are represented by the two vectors $\hat i + 2\hat j + 3\hat k$ and $3\hat i - 2\hat j + \hat k$. What is the area of parallelogram
$8$
$8\sqrt 3 $
$3\sqrt 8 $
$192$
Two adjacent sides of a parallelogram are represented by the two vectors $\hat i + 2\hat j + 3\hat k$ and $3\hat i - 2\hat j + \hat k$. What is the area of parallelogram
Area of parallelogram $ = \overrightarrow A \times \overrightarrow B $
$ = (\hat i + 2\hat j + 3\hat k) \times 3\hat i - 2\hat j + \hat k)$
$ = \left|{\,\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\1&2&3\\3&{ - 2}&1\end{array}\,} \right|$
$ = (8)\hat i + (8)\hat j - (8)\hat k$
Magnitude $ = \sqrt {64 + 64 + 64} $=$8\sqrt 3 $
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