Question

The vectors from origin to the points A and B are $\overset{\rightarrow}{A} = 3\widehat{i}–6\widehat{j} + 2\widehat{k}$ and $\overset{\rightarrow}{B} = 2\widehat{i} + \widehat{j}–2\widehat{k}$respectively. The area of the triangle OAB will be –

• A. $\frac{5}{2}\sqrt{17}$ sq. unit
• B. $\frac{2}{5}\sqrt{17}$ sq. unit
• C. $\frac{3}{5}\sqrt{17}$ sq. unit
• D. $\frac{5}{3}\sqrt{17}$ sq. unit

Answer 1

Answer: (A)

$\frac{5}{2}\sqrt{17}$ sq. unit

Answer 2

Area of D = $\frac{1}{2}\left| \overset{\rightarrow}{OA} \times \overset{\rightarrow}{OB} \right|$

= $\frac{1}{2}\left| \begin{matrix} \widehat{i} & \widehat{j} & \widehat{k} \\ 3 & –6 & 2 \\ 2 & 1 & - 2 \end{matrix} \right|$

= $\frac{1}{2}\left| (10\widehat{i} + 10\widehat{j} + 15\widehat{k}) \right| = \frac{1}{2}\sqrt{425}$ = $\frac{5}{2}\sqrt{17}$