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CGP EDU Academic Team
Published on: September 12, 2026
The area of the triangle formed by 2\hat{i} + \hat{j} - \hat{k} and \hat{i} + \hat{j} + \hat{k} is
Text Solution
Verified by ExpertsThe correct answer is:
D
\vec{A} = 2\hat{i} + \hat{j} - \hat{k}, \vec{B} = \hat{i} + \hat{j} + \hat{k}
Area of the triangle \(= \frac{1}{2} (\vec{A} \times \vec{B})\)
\(= \frac{1}{2} \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 1 & -1 \\ 1 & 1 & 1 \end{vmatrix} = \frac{1}{2} | 2\hat{i} - 3\hat{j} + \hat{k} | = \frac{1}{2} \sqrt{4 + 9 + 1}\)
\(= \frac{\sqrt{14}}{2} \text{ sq. unit}\)
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