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Vector Algebra
NCERT Class 12
CBSE
Grade 12

Question:

Show that the area of a parallelogram having diagonals $\vec{a}$ and $\vec{b}$ is $\dfrac{1}{2} |\vec{a} \times \vec{b}|$.

Step-by-Step Solution

Express $\vec{a} = \vec{u}+\vec{v}, \vec{b} = \vec{u}-\vec{v}$. [1.5 Marks]
$\vec{a}\times\vec{b} = 2(\vec{v}\times\vec{u}) \Rightarrow \text{Area} = \dfrac{1}{2}|\vec{a}\times\vec{b}|$. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Expressing diagonals in terms of side vectors: 1.5 Marks
Evaluating cross product identity and proving area formula: 1.5 Marks

Correct Answer:
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