The vectors from origin to the points $A$ and $B$ are $\overrightarrow A = 3\hat i - 6\hat j + 2\hat k$ and $\overrightarrow B = 2\hat i + \hat j - 2\hat k$ respectively. The area of the triangle $OAB$ be
The vectors from origin to the points $A$ and $B$ are $\overrightarrow A = 3\hat i - 6\hat j + 2\hat k$ and $\overrightarrow B = 2\hat i + \hat j - 2\hat k$ respectively. The area of the triangle $OAB$ be
$\frac{5}{2}\sqrt {17} $ sq.unit
$\frac{2}{5}\sqrt {17} $ sq.unit
$\frac{3}{5}\sqrt {17} $ sq.unit
$\frac{5}{3}\sqrt {17} $ sq.unit
The vectors from origin to the points $A$ and $B$ are $\overrightarrow A = 3\hat i - 6\hat j + 2\hat k$ and $\overrightarrow B = 2\hat i + \hat j - 2\hat k$ respectively. The area of the triangle $OAB$ be
Given $\overrightarrow {OA} = \overrightarrow a = 3\hat i - 6\hat j + 2\hat k$ and $\overrightarrow {OB} = \overrightarrow b = 2\hat i + \hat j - 2\hat k$
$\therefore \,\,\,(\overrightarrow a \times \overrightarrow b )\, $$= \left| {\begin{array}{*{20}{c}}{\hat i\,\,}&{\hat j\,\,}&{\hat k}\\{\,3\,\,}&{ -6\,\,\,}&2\\{\,\,\,2\,\,\,}&{1\,\,}&{ - 2\,\,\,}\end{array}}\right|\,$
$ = (12 - 2)\hat i + (4 + 6)\hat j + (3 + 12)\hat k$
$ = 10\hat i + 10\hat j + 15\hat k$$\Rightarrow \,\,|\overrightarrow a \times \overrightarrow b |\, = \,\sqrt {{{10}^2} + {{10}^2} + {{15}^2}} $
$ =\sqrt {425} $ $ = 5\sqrt {17} $
Area of $\Delta OAB = \frac{1}{2}|\overrightarrow a \times \overrightarrow b |\, =\frac{{5\sqrt {17} }}{2}\,$sq.unit.
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