Word Count : 306

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We are to compute numerically (manually) the derivative of $$ \vec{a}(t)\cdot \vec{b}(t) $$ where $$ \vec{a}(t) = (t^3 - t)\hat{i} + (3t + 4)\hat{j} + 2t^2\hat{k} $$ $$ \vec{b}(t) = (7 - t^2)\hat{i} + (4 + 6t)\hat{j} - 6t^3\hat{k} $$ and evaluate at $t = 1$. --- ### Step 1: Compute the dot product $$ \vec{a}(t)\cdot \vec{b}(t) = [(t^3-t)(7-t^2)] + [(3t+4)(4+6t)] ____ ________ __________ ________ ____ _________ ___.
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