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Prove that .
Prove that $\vec{a} \cdot [(\vec{b} + \vec{c}) \times (\vec{a} + 3\vec{b} + 4\vec{c})] = [\vec{a} \quad \vec{b} \quad \vec{c}]$.
Given: $\vec{a} \cdot [(\vec{b} + \vec{c}) \times (\vec{a} + 3\vec{b} + 4\vec{c})]$
To show: $[\vec{a} \quad \vec{b} \quad \vec{c}]$
Answer
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From ISC 2020 Mathematics Paper 1, question 16(a).