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3-1.Vectors
medium
The area of the triangle formed by $2\hat i + \hat j - \hat k$ and $\hat i + \hat j + \hat k$ is
A
$3$ sq.unit
B
$2\sqrt 3 $ sq. unit
C
$2\sqrt {14} $ sq. unit
D
$\frac{{\sqrt {14} }}{2}$ sq. unit
Solution
(d) $\vec A = 2\hat i + \hat j – \hat k,\,\,\,\,\vec B = \hat i + \hat j + \hat k\,\,$
Area of the triangle $ = \frac{1}{2}\left( {\vec A \times \vec B} \right)$
$ = \frac{1}{2}\,\left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\2&1&{ – 1}\\1&1&1\end{array}} \right|$$ = \frac{1}{2}\left| {2\hat i – 3\hat j + \hat k} \right|$$ = \frac{1}{2}\sqrt {4 + 9 + 1} $
$ = \frac{{\sqrt {14} }}{2}\,sq.\,unit$
Standard 11
Physics
