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Question 14

Let $$\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}$$, $$\vec{b} = 10\hat{i} + 2\hat{j} - \hat{k}$$ and a vector $$\vec{c}$$ be such that $$2(\vec{a} \times \vec{b}) + 3(\vec{b} \times \vec{c}) = \vec{0}$$. If $$\vec{a} \cdot \vec{c} = 15$$, then $$\vec{c} \cdot (\hat{i} + \hat{j} - 3\hat{k})$$ is equal to :

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