Vector Algebra Question - CBSE

Question

Area of a rectangle having vertices $A, B, C, D$ with position vectors $-\hat{i} + \dfrac{1}{2}\hat{j} + 4\hat{k}$, $\hat{i} + \dfrac{1}{2}\hat{j} + 4\hat{k}$, $\hat{i} - \dfrac{1}{2}\hat{j} + 4\hat{k}$ and $-\hat{i} - \dfrac{1}{2}\hat{j} + 4\hat{k}$ is:
(a) $2$ sq. units
(b) $1$ sq. unit
(c) $\dfrac{1}{2}$ sq. units
(d) $4$ sq. units

Accepted Answer

$\vec{AB} = 2\hat{i}, \vec{BC} = -\hat{j} \Rightarrow ext{Area} = |2\hat{i} imes (-\hat{j})| = 2$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Evaluating area $= 2$ sq. units: 1.0 Mark

Question:

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