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CGP EDU Academic Team
Published on: September 12, 2026
Two adjacent sides of a parallelogram are represented by the two vectors \hat{i} + 2\hat{j} + 3\hat{k} and 3\hat{i} - 2\hat{j} + \hat{k} . What is the area of parallelogram
Text Solution
Verified by ExpertsThe correct answer is:
B
Area of parallelogram \(= \vec{A} \times \vec{B}\)
\(= (\hat{i} + 2\hat{j} + 3\hat{k}) \times (3\hat{i} - 2\hat{j} + \hat{k})\)
\(= \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 2 & 3 \\ 3 & -2 & 1 \end{vmatrix} = (8)\hat{i} + (-8)\hat{j} + (8)\hat{k}\)
Magnitude \(= \sqrt{64 + 64 + 64}\) = \(8\sqrt{3}\)
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