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Find the area of the parallelogram whose sides are represented by $2 \hat{i} + 4 \hat{j} - 6 \hat{k}$ and $\hat{i} + 2 \hat{k}$

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16.4

14.4

15.4

13.4

answer is A.

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Detailed Solution

$A \times B = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 4 & - 6 \\ 1 & 0 & 2 \end{matrix}|$

$= \hat{i} (8 - 0) + \hat{j} (- 6 - 4) + \hat{k} (0 - 4) = 8 \hat{i} - 10 \hat{j} - 4 \hat{k}$

Area of parallelogram $= | A \times B |$

$= \sqrt{(8)^{2} + (10)^{2} + (4)^{2}}$

=13.4 units

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