Let \(\vec{a} = 2\hat{i} + 3\hat{j} + 3\hat{k}\), \(\vec{b} = 6\hat{i} + 3\hat{j} + 3\hat{k}\). If \(2\vec{a} + 3\vec{b}\) and \(\vec{a} - \vec{b}\) are two adjacent sides of a triangle then square of area of the triangle is
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To simplify \((m\vec{a} + n\vec{b}) \times (p\vec{a} + q\vec{b})\), use the scalar property: the result is always \((mq - np)(\vec{a} \times \vec{b})\). This saves time over calculating each vector side individually.