Question

$\overrightarrow{OA}=3i+4j+12k,\overrightarrow{OB}=12i+3j+4k,$ $\overrightarrow{OC}=4i+12j+3k.$
Find the area of triangle OAB.

• A. $\Delta OAB=\frac{1}{2}\sqrt{19345}$
• B. $\Delta OAB=19345$
• C. $\Delta OAB=\frac{1}{2}\sqrt{30085}$
• D. $\Delta OAB=30085$

Answer 1

The correct option is A $\Delta OAB=\frac{1}{2}\sqrt{19345}$

$\overrightarrow{OA}\times \overrightarrow{OB}=\left|\begin{array}{ccc}i& j& k\\ 3& 4& 12\\ 12& 3& 4\end{array}\right|=-20i+132j-39k$

$\therefore$ Area of $\Delta OAB=\frac{1}{2}|OA\times OB|=\frac{1}{2}\sqrt{[{(-20)}^2+{\left(132\right)}^2+{(-39)}^2]}=\frac{1}{2}\sqrt{19345}$