(Solved): please help Find the unit tangent vector \( T(t) \) to the curve \( r(t)=\cos (t) i+3 t j+2 \sin (2 ...

Find the unit tangent vector \( T(t) \) to the curve \( r(t)=\cos (t) i+3 t j+2 \sin (2 t) k \) when \( t=0 \). A) \( 3 j+4 k \) B) \( \frac{3}{5} \mathbf{j}+\frac{4}{5} \mathbf{k} \) C) \( 5 j+12 k \) D) \( \frac{1}{\sqrt{26}} \mathbf{i}+\frac{3}{\sqrt{26}} \mathbf{j}+\frac{4}{\sqrt{26}} \mathbf{k} \) E) \( \frac{5}{13} j+\frac{12}{13} \mathbf{k} \) F) \( \frac{1}{\sqrt{14}} \mathbf{i}+\frac{3}{\sqrt{14}} \mathbf{j}+\frac{2}{\sqrt{14}} \mathbf{k} \)