A particle is traveling along a helix whose vector equation is given by $\mathbf { r } ( t ) = \langle R \cos \alpha t , R \sin \alpha t , \beta t \rangle$ . Show that its velocity and acceleration are orthogonal at all times.

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The Answer of A particle is traveling along a helix whose vector equation is given by $\mathbf { r } ( t ) = \langle R \cos \alpha t , R \sin \alpha t , \beta t \rangle$ . Show that its velocity and acceleration are orthogonal at all times.

A Particle Is Traveling Along a Helix Whose Vector Equation r(t)=⟨Rcos⁡αt,Rsin⁡αt,βt⟩\mathbf { r } ( t ) = \langle R \cos \alpha t , R \sin \alpha t , \beta t \rangler(t)=⟨Rcosαt,Rsinαt,βt⟩

A Particle Is Traveling Along a Helix Whose Vector Equation $\mathbf { r } ( t ) = \langle R \cos \alpha t , R \sin \alpha t , \beta t \rangle$