47) Given \vecs r(t)=t \,\hat{\mathbf{i}}+2\sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf{k}} and \(\vecs u(t)=\frac{1}{t} \,\hat{\mathbf{i}}+2 \sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf...47) Given \vecs r(t)=t \,\hat{\mathbf{i}}+2\sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf{k}} and \vecs u(t)=\frac{1}{t} \,\hat{\mathbf{i}}+2 \sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf{k}}, find the following:
47) Given \vecs r(t)=t \,\hat{\mathbf{i}}+2\sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf{k}} and \(\vecs u(t)=\frac{1}{t} \,\hat{\mathbf{i}}+2 \sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf...47) Given \vecs r(t)=t \,\hat{\mathbf{i}}+2\sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf{k}} and \vecs u(t)=\frac{1}{t} \,\hat{\mathbf{i}}+2 \sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf{k}}, find the following:
47) Given \vecs r(t)=t \,\hat{\mathbf{i}}+2\sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf{k}} and \(\vecs u(t)=\frac{1}{t} \,\hat{\mathbf{i}}+2 \sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf...47) Given \vecs r(t)=t \,\hat{\mathbf{i}}+2\sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf{k}} and \vecs u(t)=\frac{1}{t} \,\hat{\mathbf{i}}+2 \sin t \,\hat{\mathbf{j}}+2 \cos t \,\hat{\mathbf{k}}, find the following: