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(Solved): Find the curvature \( K \) of the curve \( \mathbf{r}(t)=t \mathbf{i}+5 t^{2} \mathbf{j}+\frac{7 t ...
Find the curvature \( K \) of the curve \( \mathbf{r}(t)=t \mathbf{i}+5 t^{2} \mathbf{j}+\frac{7 t^{3}}{4} \mathbf{k} \) at the point \( P(2,20,14) \). Round your answer to three decimal places. a. \( 0.009 \) b. \( 9.952 \) c. \( 7.286 \) d. \( 0.021 \) e. \( 0.014 \)
Expert Answer
Solution: Given, r?(t)=ti+5t2j+7t34k------(1) Differentiating (1) w.r.t. t r??(t)=ddt(ti+5t2j+7t34k) ?r??(t)=1i+10tj+21t24k--------(2) ?r??(2)=1i+20j+