Question

Two adjacent sides of a parallelogram are represented by the two vectors $\widehat{i} + 2\widehat{j} + 3\widehat{k}$ and$3\widehat{i} - 2\widehat{j} + \widehat{k}$. What is the area of parallelogram

• A. 8
• B. $8\sqrt{3}$
• C. $3\sqrt{8}$
• D. 192

Answer 1

Answer: (A)

8

Answer 2

Area of parallelogram

$= \overset{\rightarrow}{A} \times \overset{\rightarrow}{B}$

$= (\widehat{i} + 2\widehat{j} + 3\widehat{k}) \times (3\widehat{i} - 2\widehat{j} + \widehat{k})$

\widehat{i} & \widehat{j} & \widehat{k} \\ 1 & 2 & 3 \\ 3 & - 2 & 1 \end{matrix} \right| = (8)\widehat{i} + (8)\widehat{j} - (8)\widehat{k}$$ Magnitude $= \sqrt{64 + 64 + 64}$=$8\sqrt{3}$