Given $\displaystyle f(t)=(\cos t,\sin t,t)$ then find the tangent line and normal plane if $\displaystyle f\left( \dfrac{\pi }{4} \right)=\left( \dfrac{1}{\sqrt{2}},\dfrac{1}{\sqrt{2}},\dfrac{\pi }{4} \right).$

Let $\displaystyle x(t)=\cos t,y(t)=\sin t,z(t)=t$ so normal plane is given by

$\displaystyle \left\langle \left( x'\left( {{t}_{0}} \right),y'\left( {{t}_{0}} \right),z'\left( {{t}_{0}} \right) \right),\left( x-x\left( {{t}_{0}} \right),y-y\left( {{t}_{0}} \right),z-z\left( {{t}_{0}} \right) \right) \right\rangle =0.$ Is that correct?

How to find the tangent line?