For $\vec { r } ( t ) = \left\langle \sin \left( \frac { \pi } { 2 } t \right) , \cos \left( \frac { \pi } { 2 } t \right) , t \right\rangle$ find the displacement vector as $t$ goes from $t = - 1$ to $t = 1$

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The Answer of For $\vec { r } ( t ) = \left\langle \sin \left( \frac { \pi } { 2 } t \right) , \cos \left( \frac { \pi } { 2 } t \right) , t \right\rangle$ find the displacement vector as $t$ goes from $t = - 1$ to $t = 1$

For r⃗(t)=⟨sin⁡(π2t),cos⁡(π2t),t⟩\vec { r } ( t ) = \left\langle \sin \left( \frac { \pi } { 2 } t \right) , \cos \left( \frac { \pi } { 2 } t \right) , t \right\rangler(t)=⟨sin(2π​t),cos(2π​t),t⟩

For $\vec { r } ( t ) = \left\langle \sin \left( \frac { \pi } { 2 } t \right) , \cos \left( \frac { \pi } { 2 } t \right) , t \right\rangle$