Consider r(t)=⟨sin(t),cos(t),2t⟩ the position vector of a particle at time t∈[0,3], where the components of r are expressed in centimeters and time is measured in seconds. Let OP−→− be the position vector of the particle after 1 sec. Find the scalar equation of the plane that is perpendicular to v(1) and passes through point P. This plane is called the normal plane to the path of the particle at point P.

Consider r(t)=⟨sin(t),cos(t),2t⟩ the position vector of a particle at time t∈[0,3], where the components of r are expressed in centimeters and time is measured in seconds. Let OP−→− be the position vector of the particle after 1 sec. Find the scalar equation of the plane that is perpendicular to v(1) and passes through point P. This plane is called the normal plane to the path of the particle at point P.